Free Printable Transformations Review

1.

Find the equation that matches this graph.

a)

$y=5\sqrt{x}$

b)

$y=\sqrt{x+5}$

c)

$y=\sqrt{x}+5$

d)

$y=\sqrt{x-5}$

e)

$y=\sqrt{x}-5$

2.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

3.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

4.

What does the equation

g\left(x\right)\ =\ f\left(x\right)-4\

do to the graph of f(x)?

a)

Shifts the graph left four units

b)

Shifts the graph right four units

c)

Shifts the graph up four units

d)

Shifts the graph down four units

5.

The linear parent function, f(x) = x, is transformed to g(x) = f(x - 3). Describe the transformation.

a)

g(x) is shifted up 3 units

b)

g(x) is shifted down 3 units

c)

g(x) is shifted left 3 units

d)

g(x) is shifted right 3 units

6.

Given g(x) is obtained by transforming of h(x) and $g\left(x\right)=h\left(x-1\right)+2$ , describe the transformations on $h\left(x\right).$

a)

translated 1 unit left and 2 units up

b)

translated 1 unit right and 2 units up

c)

translated 2 units left and 1 unit up

d)

translated 2 units right and 1 unit up

7.

Describe the transformation of the graph
y = -(x + 4)³ + 5

a)

Up 5 and Left 4

b)

Reflect x-axis, Left 4, Up 5

c)

Reflect x-axis, Right 4, Up 5

d)

Right 4 and up 5

8.

Which of the following is the graph of $y=\left(x-4\right)^3+2$

a)

b)

c)

d)

9.

Reflect this point over the x-axis.

(2, 3)

a)

(2, -3)

b)

(-2, -3)

c)

(-2, 3)

10.

Reflect this point over the y-axis.

(2, 3)

a)

(2, -3)

b)

(-2, -3)

c)

(-2, 3)

11.

Find the equation of the line reflected across the x-axis.

y = 3x + 2

a)

y = 3x + 2

b)

y = 3x - 2

c)

y = -3x - 2

d)

y = -3x + 2

12.

Find the equation of the line reflected across the y-axis.

y = 3x + 2

a)

y = 3x + 2

b)

y = 3x - 2

c)

y = -3x - 2

d)

y = -3x + 2

13.

What does the equation $g\left(x\right)=2f\left(x\right)\$ do to the graph of f(x)?

a)

Moves the graph up 2 units

b)

Vertical stretch of scale factor 2

c)

Reflects the graph across the x-axis

d)

Moves the graph 2 units to the left

14.

Identify the transformation of f(x) = x²to g(x) = 0.5x²

a)

Stretch

b)

Reflection

c)

Compression

15.

What is the equation of the absolute value function?

a)

f(x)= 4|x+3|

b)

f(x)= 1/4 |x+3|

c)

f(x)= 1/4 |x - 3|

d)

f(x)= 4|x - 3|

16.

How would the graph of f(x) = 1.5|x|compare to graph of g(x) = |x|?

a)

The graph of f(x) would be more narrow.

b)

The graph of fx) would be wider.

17.

Identify the transformation of f(x) = x²to g(x) = 0.5x²

a)

Stretch

b)

Reflection

c)

Compression

18.

Identify the transformation of f(x) = x²to g(x) = -x²

a)

Stretch

b)

Reflection

c)

Compression

19.

If the blue graph is the parent function, what vertical transformation has to happen in order for it to become the green function

a)

compression

b)

stretch

c)

reflection

d)

shift up

20.

Identify the transformations

y = 2|x - 2| - 2.

a)

stretch of 2; right 2; down 2

b)

stretch of 2; left 2; down 2

c)

compression of 2; left 2; up 2

d)

compression of 2; right 2, down 2

21.

Describe the transformation of the quadratic function.

Parent Function: $y\ =\ x^2$

Transformed Function: $y\ =\ \frac{1}{4}x^2$

a)

Vertical stretch of $\frac{1}{4}$ , making the graph more narrow

b)

Vertical compression of $\frac{1}{4}$ , making the graph wider

c)

Vertical reflection of $\frac{1}{4}$ , flipping the graph over the x-axis.

d)

Vertical reflection of $\frac{1}{4}$ , flipping the graph over the y-axis.

22.

If the point $\left(-6,\ 10\right)$ lies on the graph of $y=f\left(x\right)$ then which of the following points MUST lie on the graph of $y=\frac{1}{2}f\left(x\right)$ ?

a)

$\left(-3,\ 5\right)$

b)

$\left(-3,\ 10\right)$

c)

$\left(-6,\ 5\right)$

d)

$\left(-12,\ 20\right)$

23.

If the graph of $y=x^2$ is vertically compressed by a factor of 1/3 and then shifted 4 units down, the resulting graph would have an equation of

a)

$y=\frac{1}{3}x^2-4$

b)

$y=-3x^2-4$

c)

$y=-4x^2-3$

d)

$y=-\frac{1}{3}x^2+4$

24.

What is the domain of the graph?

a)

x ≥ -6

b)

-7 ≤ x ≤ 3

c)

-8 ≤ x ≤ 4

d)

x ≤ -6

e)

All real numbers

25.

What is the range of the graph?

a)

y ≥ -6

b)

-7 ≤ y ≤ 3

c)

-8 ≤ y ≤ 4

d)

y ≤ -6

e)

All real numbers

Transformations Review

Total questions: 25

Worksheet time: 25mins

Similar Resources on Wayground