Describe how the graph of f(x)=|x| can be transformed to the graph of g(x)=−14|x−1|+1.
A. g(x) is reflected and vertically compressed, the graph shifts to the right 1 unit and then up 1 unit.
B. g(x) is reflected and vertically stretched, the graph shifts to the right 1 unit and then down 1 unit.
C. g(x) is reflected and vertically stretched, the graph shifts left 1 unit and then up 1 unit.
D. g(x) is reflected and vertically compressed, the graph shifts left 1 unit and then down 1 unit.
Answers
Answer:
N/A, but A if anything
Step-by-step explanation:
Let's start with the change within the absolute value.
In f(x), x is turned into x-1. There is no other way to add the -1 into the absolute value.
Therefore, our first transformation is f(x) -> f(x-1). In f(x+C), the graph is moved to the left by c units. Therefore, as C = -1, the graph is shifted to the right by 1 unit.
Next, we can move to the 14. Given that f(x-1) = |x-1|, we can see that we multiply 14 to f(x). Cf(x) vertically stretches a function if C is greater than 0, which 14 is, so the graph is vertically stretched.
After that, we have the negative. This happens outside the absolute values, so it is reflected in -f(x), not f(-x). This reflects a function across the x axis, but all we need to know for this question is that it is reflected.
Finally, we have the +1. This happens outside the absolute values, so it is reflected in f(x) + C, not f(x+C). The value of C moves the graph up by C units, and the +1 therefore moves the graph up by 1 unit.
We thus know 4 things:
1. The graph goes up by 1 units
2. The graph is reflected across the x axis
3. The graph is stretched vertically
4. The graph is shifted to the right by 1 unit
None of the answers given fit these, but A comes the closest.
Related Questions
If the length and breadth of a rectangle are 10cm and 20cm, respectively, find the length of its diagonal. Pls guys help me! Step-by-Step Explanation!
Answers
Redraw diagram with just triangle and labels
Use Pythagoras formula : x^2= a^2 +b^2
Sub in respective values
By solving, ans: 20. 36cm to 2dp
If the number of tomato growers in the market increases, the supply:
A) of tomatoes increases.
B) of tomatoes decreases.
C) tomatoes remains constant.
D) curve for tomatoes shifts to the left.
Answers
If the number of tomato growers in the market increases, it would generally lead to an increase in the supply of tomatoes increases.
The correct answer is A.
This is because an increase in the number of growers means that there are more producers entering the market, resulting in a greater quantity of tomatoes available for sale. As a result, the overall supply of tomatoes would increase.In terms of the supply curve, an increase in the number of growers would cause the supply curve for tomatoes to shift to the right. This signifies that at any given price, there would be a larger quantity of tomatoes supplied in the market. Consequently, consumers would have access to a greater supply of tomatoes, potentially leading to lower prices due to the increased competition among the growers. Thus, supply of tomatoes increases accurately reflects the likely outcome when the number of tomato growers increases.The correct answer is A.
For such more questions on tomatoes
https://brainly.com/question/17127567
#SPJ8
Write a short paragraph explaining at least one experience how math has been applied during your spring break.
Answers
Answer:
Figuring out the amount of money needed to pay for a product at the store.
Step-by-step explanation:
Express the ratio below in its simplest form
12:6
Answers
Answer:
12/6 simplified to lowest terms is 2/1.
Step-by-step explanation:
Divide both the numerator and denominator by the HCF
12 ÷ 6
6 ÷ 6
Reduced fraction:
12/6 simplified to lowest terms is 2/1.
Answer: 2:1
Step-by-step explanation:
12:6
Both left and right can be divided by 6, like a fraction, reduce.
= 2:1
Use the leading coefficient and degree of the polynomial function f(x) = x3 – 7x2 + 10x to determine the end behavior of its graph. Select all the correct statements. A. As x → ∞, y → ∞. B. As x → ∞, y → −∞. C. As x → −∞, y → ∞. D. As x → −∞, y → −∞. E. As x → ∞, y → 0.
Answers
Given:
The function is
\(f(x)=x^3-7x^2+10x\)
To find:
The end behavior of its graph.
Solution:
We have,
\(f(x)=x^3-7x^2+10x\)
Here, leading coefficient is 1 which is positive and degree of function is 3 which is odd.
For odd degree and positive leading coefficient, the end behavior is
\(f(x)\to \infty\text{ as }x\to \infty\)
\(f(x)\to -\infty\text{ as }x\to -\infty\)
Using this, we get
\(\text{As }x\to \infty, y\to \infty\)
\(\text{As }x\to -\infty, y\to -\infty\)
Therefore, the correct statements are A and D.
We want to study the end behavior of the given polynomial.
The two correct statements are A and D.
As x → ∞, y → ∞As x → −∞, y → −∞The polynomial is:
f(x) = x^3 - 7*x^2 + 10*x.
We can see that the degree of this polynomial is odd, this means that the behavior on the negative side is opposite to the one in the positive side.
In this case, the leading coefficient is one, so it is positive. This will mean that, for large positive values of x, f(x) will be positive.
For large (in absolute value) negative values of x, f(x) will be negative.
Then the end behavior is given by:
As x → ∞, y → ∞As x → −∞, y → −∞So the two correct statements are A and D.
If you want to learn more, you can read:
https://brainly.com/question/22723521
At a pizza eating competition, Davonne at two more than twice as many slices as the runner-up. If Davonne at 11 slices, then how many slices did the runner-up eat?
Answers
solve for brainliest
Answers
Answer:
7) 9.135x10^10
8) 3.428x10^-2
9) 2.5x10^-7
10) 4x10^10
Step-by-step explanation:
You’re only supposed to have one number to the left of the decimal point in scientific notation.
7) 9.135x10^10
8) 3.428x10^-2
9) 2.5x10^-7
10) 4x10^10
the distance between my house and my school is 8 miles and takes 10 minutes by bus.How fast is the bus?
Answers
Answer:
The bus travels at 48 miles per hour.
Step-by-step explanation:
It is given that:
Distance between school and house = 8 miles
Time taken by bus = 10 minutes = \(\frac{10}{60}=\frac{1}{6}\ hour\)
Speed of bus = \(\frac{distance}{time}\)
Speed of bus = \(\frac{8}{\frac{1}{6}}\)
Speed of bus = 8*6 miles per hour
Speed of bus = 48 miles per hour
Therefore,
The bus travels at 48 miles per hour.
Find the equation of the line shown (first to do gets brainlist)
Answers
Answer:
y = -2x + 9
Step-by-step explanation:
A politician claims that he is supported by a clear majority of voters. In a recent survey, 41 out of 70 randomly selected voters indicated that they would vote for the politician. a. Select the null and the alternative hypotheses. He: p = 0.50; HA: p0.50 NO: P = 0.50; HA: p > 0.50 He: p = 0.50; HA: P < 0.50 b.
Answers
The null and the alternative hypotheses are NO: P = 0.50; HA: p > 0.50. Option B
How to determine the hypothesisThe null hypothesis postulates that the politician lacks the support of a significant majority of voters. The hypothesis that opposes the initial one suggests that the politician has gained ample support from a significant number of voters.
The null hypothesis represents an equality statement, whereas the alternative hypothesis represents an inequality statement.
The null hypothesis postulates that the percentage of voters who endorse the politician is identical to 0. 50, which is the percentage that would be anticipated if he lacked significant backing. The alternative hypothesis suggests that there is a higher proportion of voters who endorse the politician compared to the anticipated 0. 50 proportion of voters who would sympathize with the politician if he had a decisive majority.
The results of the survey provide evidence in favor of the alternate hypothesis. Amongst 70 voters chosen at random, 41 individuals disclosed their intention to vote for the politician.
Then, we have to reject the null hypothesis
Learn more about null hypothesis at: https://brainly.com/question/4436370
#SPJ1
HELP PLEASE
18 miles= how many feet
_________feet
Answers
Answer:
18 miles= how many feet
____95,040_____feet
Step-by-step explanation:
happy to help ya:)
What is the name of the relationship between angle 5 and angle 7?
1) corresponding
2) vertical
3) supplementary
4) alternate exterior
Answers
vertical angles are always across from each other where two lines cross
angle 6 and angle 8 are also vertical
angle 1 and angle 3 are also vertical
angle 4 and angle 2 are also vertical
hope this helps :)
the sum of the square of two consecutive positive integers is 85. Write a quadratic equation
Answers
Answer:
2x^2 + 2x - 83 = 0
Step-by-step explanation:
Consecutive integers differ by 1
Let the first number be x
The next will be (x+1)
The sum of the squares of these two numbers is 85
so we have;
x^2 + (x + 1)^2 =85
= x^2 + x^2 + 2x + 2 = 85
2x^2 + 2x + 2-85 = 0
2x^2 + 2x - 83 = 0
How many solutions does the following system have?
y = 2/3x +3
- 2x + 3y = 9
Answers
(WORK SHOWN BELOW)
if the power series an(x-4)^n converges at x=7 and diverges at x=9
Answers
The power series an(x-4)^n converges at x=7 and diverges at x=9. This means that when x=7, the series converges to a finite value, while at x=9, it diverges to infinity or negative infinity.
To determine the values of a and the radius of convergence, we need to use the ratio test. The ratio test states that the series converges if the limit of the ratio of the absolute values of consecutive terms is less than 1. The radius of convergence can be found by taking the limit of the ratio of the absolute values of consecutive terms as n approaches infinity. Since the series converges at x=7 and diverges at x=9, we can conclude that the radius of convergence is between 4 and 5. However, we cannot determine the exact value of the radius of convergence without additional information.
To know more about convergence visit:
https://brainly.com/question/31756849
#SPJ11
Write the equation of the line in slope-intercept form.
Answers
Answer:
\(consider : (7, 0) \: and \: (0, 70) \\ m = \frac{(70 - 0)}{(0 - 7)} \\ m = - 10 \\ y = mx + c \\ 0 = ( - 10 \times 7) + c \\ c = 70 \\ \therefore \: \: y = - 10x + 70\)
What is the y-intercept of f(x) = (1/2)^x?
A. (0, 1)
B. (1,0)
C. (1, 1/2)
D. (0,0)
Answers
Answer:
A. (0, 1)
Step-by-step explanation:
You want to know the y-intercept of f(x) = (1/2)^x.
Y-interceptThe y-intercept of a function is the function value when x=0. Put 0 where x is and do the arithmetic.
f(0) = (1/2)^0
f(0) = 1
The y-intercept is (x, f(x)) = (0, f(0)) = (0, 1).
__
Additional comment
Any non-zero value to the zero power is 1.
<95141404393>
The path of a baseball after it has been hit is modeled by the function h = – 0. 32d2 + d + 3, where h is the height in feet of the baseball and d is the distance in feet the baseball is from home plate. What is the maximum height reached by the baseball, round your answer to the nearest hundredths? (Hint: Find the y-coordinate of the equation. )
Answers
The maximum height reached by the baseball is approximately 7.66 feet.
The maximum height reached by the baseball can be found by determining the vertex of the function h = -0.32d^2 + d + 3.
The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b/2a. In this case, a = -0.32 and b = 1.
To find the maximum height, we need to find the y-coordinate of the vertex, which corresponds to the height (h) in this problem.
Using the formula x = -b/2a, we can calculate the x-coordinate of the vertex:
d = -1/(2 * (-0.32))
d ≈ 1.5625
To find the corresponding height, we substitute this value back into the function:
h = -0.32(1.5625)^2 + 1.5625 + 3
h ≈ 3.09375 + 1.5625 + 3
h ≈ 7.65625
Rounding this value to the nearest hundredths, the maximum height reached by the baseball is approximately 7.66 feet.
Learn more about height here
https://brainly.com/question/28990670
#SPJ11
The diameter of a circular pool is 18 feet, how much land does the pool take up?
PLEASE HELP ME
Answers
Work Shown:
d = 18 = diameter
r = d/2 = 18/2 = 9 = radius
A = area of a circle of radius r
A = pi*r^2
A = 3.14*9^2
A = 254.34
The pool takes up approximately 254.34 square feet of area. Use more decimal digits of pi to get a more accurate answer.
As a retiring employee, you'll receive 8.96% of your average salary from the last five years you worked with your company.
You plan to retire after 36 years with the company.
Your salaries for your last five years are:
$140,647
$201,419
$138,739
$134,820
$182,896
Calculate your annual retirement salary.
Answers
Answer:
$134,820
Step-by-step explanation:
is the correct answer
explain how bacteria are both helpful and harmful to out bodies
Answers
Answer:
Step-by-step explanation:
Bacteria is helpful because it helps protect the cells in your intestines. Its, harmful because itI can cause a disease in your lungs.
Hope this helps!
2-Nail files cost $0.61 each. Olivia buys 5 nail files. How much does Olivia spend?
3-Peter earns $10 per hour working as a plumber. How much money will he earn if he works 5 hours?
Answers
ABCD represents the plan of a field.
There is a path across the field that
starts at a
is the same distance from BA and BC.
Using ruler and compasses, show the position of the path.
Answers
A quadrilateral is a polygon with 4 number of sides and 4 vertices. The shape of the field is either square or a rhombus.
What is a quadrilateral?A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.
Given that ABCD represents a field, therefore, the field is a quadrilateral. Now, as the path is going between the field. And starts from A therefore, it will end at C.
Since It is the same distance from BA and BC. Therefore, it will be the diagonal of the quadrilateral. And as BA and BC are consecutive sides and are of the same length.
Hence, the shape of the field is either square or a rhombus.
Learn more about Quadrilateral:
https://brainly.com/question/13805601
#SPJ1
Which polynomial matches the expression -x (x – 3)?
Answers
Answer:
=> -x² + 3x
Step-by-step explanation:
-x (x – 3)
=> -x² + 3x
if p(a) = 0.62, p(b) = 0.47, and p(a è b) = 0.88, then p(a ç b) =
a. 0.2914
b. 1.9700
c. 0.6700
d. 0.2100
Answers
Answer: a
Step-by-step explanation:a
A new projector for the classroom costs $358.25. The tax rate is 12%. How much will
the tax cost for the projector?
$4299
$42.99
$346.25
DELL
$29.85
$401.24
Sign out
USD 1:33
Answers
PLSSS HELP ASAP DUE TMR MORNING
Answers
Step-by-step explanation:
Hey there!
Here;
Diameter (d) = 13 ft
Radius (r) = 13/2 = 6.5 ft
Now,
Area of a circle= πr²
= (22/7)*(6.5)²
= 132.78 ft²
Therefore, the area is 133 ft².
Hope it helps!
Step-by-step explanation:
Hey there!
Here;
Diameter (d) = 13 ft
Radius (r) = 13/2 = 6.5 ft
Now,
Area of a circle= πr²
= (22/7)*(6.5)²
= 132.78 ft²
Therefore, the area is 133 ft².
Hope it helps!
suppose a sample of 211 tankers is drawn. of these ships, 146 did not have spills. using the data, construct the 80% confidence interval for the population proportion of oil tankers that have spills each month. round your answers to three decimal places.
Answers
We can use the sample proportion of tankers without spills (146/211 = 0.692) to estimate the population proportion of tankers without spills. To construct the confidence interval, we need to find the margin of error and the critical value for an 80% confidence level.
Follow these steps:
1. Calculate the sample proportion:
In the sample of 211 tankers, 146 did not have spills, so 211 - 146 = 65 tankers had spills. The sample proportion (p-hat) is the number of tankers with spills divided by the total sample size:
p-hat = 65/211 ≈ 0.308
2. Determine the z-score for an 80% confidence interval:
Using a z-table or calculator, the z-score for an 80% confidence interval is approximately 1.282.
3. Calculate the standard error:
The standard error (SE) can be calculated using the formula: SE = sqrt(p-hat*(1-p-hat)/n)
SE = sqrt(0.308*(1-0.308)/211) ≈ 0.030
4. Construct the confidence interval:
Lower limit = p-hat - (z-score * SE)
Upper limit = p-hat + (z-score * SE)
Lower limit = 0.308 - (1.282 * 0.030) ≈ 0.277
Upper limit = 0.308 + (1.282 * 0.030) ≈ 0.339
So, the 80% confidence interval for the population proportion of oil tankers that have spills each month is approximately (0.277, 0.339), rounded to three decimal places.
To learn more about critical value :brainly.com/question/30168469
#SPJ11
helppppppppppppppppppp
Answers
Answer:
vertical opposite angles are always equal
= 143°
co-interior angles are supplementary ( 180° )
∴ x = 180 - 143 = 37
∴ x = 37°
hope this answer helps you.....
please mark as brainliest.. thank you!
Which ordered pair is a solution of the equation?
y = 82 + 3