Which correctly expresses the relationship between the two functions g ( x ) g\left(x\right) g ( x ) and h ( x ) h\left(x\right) h ( x )

h ( x ) = g ( x ) − 2 h\left(x\right)=g\left(x\right)-2 h ( x ) = g ( x ) − 2

h ( x ) = g ( x ) + 2 h\left(x\right)=g\left(x\right)+2 h ( x ) = g ( x ) + 2

g ( x ) = h ( x ) − 2 g\left(x\right)=h\left(x\right)-2 g ( x ) = h ( x ) − 2

g ( x ) = h ( x + 2 ) g\left(x\right)=h\left(x+2\right) g ( x ) = h ( x + 2 )

The rate of change is constant in the graph. Find the rate of change and then explain what it means in this context.

− 100 3 -\frac{100}{3} − 3 1 0 0 ; the value drops $100 every 3 years.

-100; the value drops $100 every year

-3; the value drops $3 every year

-1; the value drops $1 every year.

Courtney is conducting a science experiment that is measuring bacteria in a test tube. Over a number of hours, t, the number of bacteria is increasing, as indicated on the graph. Based on the graph from the experiment, which statements are true? Select all that apply.

After 4 hours, there will be 800,000 bacteria in the test tube.

There were 50,000 bacteria at the beginning of the experiment.

For 1 ≤ t ≤ 2 the rate of change is 100,000 bacteria per hour.

For 1 ≤ t ≤ 2 the rate of change is 50,000 bacteria per hour.

The number of bacteria is increasing by 50,000 every hour.

The graph represents the change in the amount of snowfall over a period of time in a single day. Which unit would be appropriate for the rate of change in the graph?

i n c h e s h o u r s \frac{inches}{hours} h o u r s i n c h e s

h o u r s i n c h e s \frac{hours}{inches} i n c h e s h o u r s

i n c h e s d a y s \frac{inches}{days} d a y s i n c h e s

s n o w h o u r s \frac{snow}{hours} h o u r s s n o w

The graph represents the change in the amount of the battery's capacity (in % charged) as a function of time (in minutes). Which unit would be appropriate for the rate of change in the graph?

c a p a c i t y min ⁡ u t e s \frac{capacity}{\min utes} min u t e s c a p a c i t y

c a p a c i t y d a y s \frac{capacity}{days} d a y s c a p a c i t y

d a y s c a p a c i t y \frac{days}{capacity} c a p a c i t y d a y s

min ⁡ u t e s c a p a c t i y \frac{\min utes}{capactiy} c a p a c t i y min u t e s

Which of the following statements are true? Select all that apply.

The graph is increasing when the domain is -6 < x < -4

The graph is decreasing when x ≤ -6

The graph is positive on the interval x > -6

The y-intercept of the function is (4, 0)

Which of the following statements are true? Select all that apply.

The graph is negative on the interval 6 < x ≤ 7

The graph is degreasing on the interval -2 ≤ x ≤ 0

The graph is increasing when x < -2

Transformations, functions, and rate of change

Authored by Emily Ruedas

Mathematics

9th Grade

CCSS covered

Used 24+ times

Transformations, functions, and rate of change

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25 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=x^2-\frac{9}{7}$ from the parent function $f\left(x\right)=x^2$

Vertical Reflection

Vertical Translation

Horizontal Translation

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=-x^2$ from the parent function $f\left(x\right)=x^2$

Vertical Reflection

Vertical Translation

Horizontal Translation

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=\left(x+3\right)^2$ from the parent function $f\left(x\right)=x^2$

Vertical Reflection

Vertical Translation

Horizontal Translation

Tags

CCSS.HSF.BF.B.3

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=\left(x+1\right)^2+13$ from the parent function $f\left(x\right)=x^2$

Vertical Reflection

Vertical Translation

Horizontal Translation

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The absolute value parent function is graphed. Which of the following statements is true based on the parent function?

The graph representing the function $f\left(x\right)=\left|x+3\right|+5$ is the graph of the parent function translated 3 units to the right and 5 units downward.

The graph representing the function $f\left(x\right)=\left|x+3\right|+5$ is the graph of the parent function translated 3 units to the right and 5 units upward.

The graph representing the function $f\left(x\right)=\left|x-3\right|+5$ is the graph of the parent function translated 3 units to the right and 5 units upward.

The graph representing the function $f\left(x\right)=\left|x-3\right|+5$ is the graph of the parent function translated 3 units to the left and 5 units upward.

Tags

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

CCSS.HSF.IF.A.1

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The quadratic parent function is graphed. Which of the following statements is true based on the parent function?

The graph representing the function $f\left(x\right)=\left(x-2\right)^2+3$ is the graph of the parent function translated 2 units to the right and 3 units downward.

The graph representing the function $f\left(x\right)=\left(x+1\right)^2-2$ is the graph of the parent function translated 1 unit to the left and 2 units downward

The graph representing the function $f\left(x\right)=\left(x-3\right)^2-4$ is the graph of the parent function translated 3 units to the left and 4 units upward.

The graph representing the function $f\left(x\right)=\left(x+5\right)^2+1$ is the graph of the parent function translated 5 units to the right and 1 unit upward.

Tags

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.C.7

CCSS.HSA.SSE.A.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which transformation will shift the function graphed to the right 2 units?

$f\left(x+2\right)$

$f\left(x\right)+2$

$f\left(x-2\right)$

$f\left(x\right)-2$

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which correctly expresses the relationship between the two functions $g\left(x\right)$ and $h\left(x\right)$

$h\left(x\right)=g\left(x\right)-2$

$h\left(x\right)=g\left(x\right)+2$

$g\left(x\right)=h\left(x\right)-2$

$g\left(x\right)=h\left(x+2\right)$

Tags

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.C.7

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function $f\left(x\right)=\left(x-3\right)^2+4$ was translated into the new function $g\left(x\right)=\left(x-3\right)^2+9$ Describe the translation.

The graph of f(x) had a vertical translation of 5 units down

The graph of f(x) had a vertical translation of 5 units up

The graph of f(x) had a vertical translation of 2 units up

The graph of f(x) had a vertical translation of 2 units down

Tags

CCSS.HSF.BF.B.3

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Transformations, functions, and rate of change

Select the answer choice(s) that best represent the transformation of the function f(x)=x2−97f\left(x\right)=x^2-\frac{9}{7}f(x)=x2−79​ from the parent function f(x)=x2f\left(x\right)=x^2f(x)=x2

Select the answer choice(s) that best represent the transformation of the function f(x)=−x2f\left(x\right)=-x^2f(x)=−x2 from the parent function f(x)=x2f\left(x\right)=x^2f(x)=x2

Select the answer choice(s) that best represent the transformation of the function f(x)=(x+3)2f\left(x\right)=\left(x+3\right)^2f(x)=(x+3)2 from the parent function f(x)=x2f\left(x\right)=x^2f(x)=x2

Select the answer choice(s) that best represent the transformation of the function f(x)=(x+1)2+13f\left(x\right)=\left(x+1\right)^2+13f(x)=(x+1)2+13 from the parent function f(x)=x2f\left(x\right)=x^2f(x)=x2

The absolute value parent function is graphed. Which of the following statements is true based on the parent function?

The quadratic parent function is graphed. Which of the following statements is true based on the parent function?

Which transformation will shift the function graphed to the right 2 units?

Which correctly expresses the relationship between the two functions g(x)g\left(x\right)g(x) and h(x)h\left(x\right)h(x)

The function f(x)=(x−3)2+4f\left(x\right)=\left(x-3\right)^2+4f(x)=(x−3)2+4 was translated into the new function g(x)=(x−3)2+9g\left(x\right)=\left(x-3\right)^2+9g(x)=(x−3)2+9 Describe the translation.

Evaluate the piecewise function for w(-1).

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Discover more resources for Mathematics

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=x^2-\frac{9}{7}$ from the parent function $f\left(x\right)=x^2$

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=-x^2$ from the parent function $f\left(x\right)=x^2$

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=\left(x+3\right)^2$ from the parent function $f\left(x\right)=x^2$

Select the answer choice(s) that best represent the transformation of the function $f\left(x\right)=\left(x+1\right)^2+13$ from the parent function $f\left(x\right)=x^2$

Which correctly expresses the relationship between the two functions $g\left(x\right)$ and $h\left(x\right)$

The function $f\left(x\right)=\left(x-3\right)^2+4$ was translated into the new function $g\left(x\right)=\left(x-3\right)^2+9$ Describe the translation.