Free Printable Transformations of Linear Functions

1.

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

a)

The graph of g is a vertical translation 2 units up of the graph of f

b)

The graph of f is a horizontal translation two units left of g

c)

The graph of g is a vertical stretch by a factor of 2 of the graph of f

d)

The graph of g is a reflection of the graph of f

2.

Which transformation will occur if f(x) = x is replaced with 2f(x)?

a)

Vertical stretch by a factor of 2

b)

Vertical compression by a factor of 1/2

c)

Vertical translation up by 2 units.

d)

Horizontal compression by a factor of 1/2

3.

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

a)

Translation left 2 units

b)

Translation right 2 units

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

4.

How did the equation shift from the parent function?

y = f(x) + c

a)

Shifted up "c" units

b)

Shifted down "c" units

c)

Stretches vertically

d)

Shifted right "c" units

5.

How did the equation shift from the parent function? y = f(x - 4)

a)

Shift right by 4

b)

Shift left by 4

c)

Horizontal Stretch by 4

d)

Vertical Stretch by 4

e)

Shift down by 4

6.

What is the linear parent function?

a)

y = x

b)

y = mx + b

c)

f(x) = 2x

d)

Not here

7.

The graphs of linear functions f and g are shown on the grid.

Which function is best represented by the graph of g?

a)

$g\left(x\right)\ =\ f\left(x\right)-6$

b)

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

c)

$g\left(x\right)=f\left(x\right)-3$

d)

$g\left(x\right)=\frac{1}{4}f\left(x\right)$

8.

The graphs of linear functions f and g are shown on the grid.

Which function is best represented by the graph of g?

a)

$g\left(x\right)=f\left(x\right)+4$

b)

$g\left(x\right)=f\left(x\right)+5$

c)

$g\left(x\right)=3f\left(x\right)$

d)

$g\left(x\right)=\frac{1}{3}f\left(x\right)$

9.

A student graphed

f\left(x\right)=x

and

g\left(x\right)=f\left(x\right)+8

on the same coordinate grid.
Which statement describes how the graphs of f and g are related?

a)

The graph of f is steeper than the graph of g.

b)

The graph of f is less steep than the graph of g.

c)

The graph of f is shifted 8 units up to create the graph of g.

d)

The graph of f is shifted 8 units down to create the graph of g.

10.

A student graphed $f\left(x\right)=x$ and $g\left(x\right)=f\left(x\right)-6$ on the same coordinate grid.
Which statement describes how the graphs of f and g are related?

a)

The graph of f is shifted 6 units down to create the graph of g.

b)

The graph of f is less steep than the graph of g.

c)

The graph of f is shifted 6 units up to create the graph of g.

d)

The graph of f is steeper than the graph of g.

11.

$f\left(x\right)=x$ and $g\left(x\right)=2x-4$
Which statement about the relationship of these two graphs is true?

a)

The graph of g is steeper than the graph of f, and the y-intercept has been translated up.

b)

The graph of g is less steep than the graph of f, and the y-intercept has been translated up.

c)

The graph of g is less steep than the graph of f, and the y-intercept has been translated down.

d)

The graph of g is steeper than the graph of f, and the y-intercept has been translated down.

12.

$f\left(x\right)=x$ and $g\left(x\right)=-\frac{2}{3}x$
Which statement about the relationship between these two graphs is true?

a)

The graph of g is less steep than the graph of f.

b)

The graph of g is less steep than the graph of f, and is reflected.

c)

The graph of g is reflected, and the y-intercept is translated down.

d)

The graph of g is steeper than the graph of f, and is reflected.

13.

$f\left(x\right)=x$ and $g\left(x\right)=-x+7$
Which statement about the relationship between these two graphs is true?

a)

The graph of g is reflected and is translated up.

b)

The graph of g is steeper than the graph of f and is reflected.

c)

The graph of g is less steep than the graph of f.

d)

The graph of g is reflected and is translated down.

14.

If $f\left(x\right)=x$ and a new line, $g\left(x\right)$ is created by changing the slope to 3 and the y-intercept to -1, which statement about the relationship between these two graphs is true?

a)

The graph of g is steeper than the graph of f, and the y-intercept is translated down.

b)

The graph of g is steeper than the graph of f, and the y-intercept is translated up.

c)

The graph of g is less steep than the graph of f, and the y-intercept is translated down.

d)

The graph of g is less steep than the graph of f, and the y-intercept is translated up.

15.

The graphs of linear functions f and g are shown on the grid. Which function is best represented by the graph of g?

a)

$g\left(x\right)=f\left(x\right)$

b)

$g\left(x\right)=\frac{1}{2}f\left(x\right)$

c)

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

d)

$g\left(x\right)=f\left(x\right)+5$

16.

The graphs of linear functions f and g are shown on the grid. Which function is best represented by the graph of g?

a)

$g\left(x\right)=-f\left(x\right)+6$

b)

$g\left(x\right)=f\left(x\right)+6$

c)

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

d)

$g\left(x\right)=-f\left(x\right)-6$

17.

Linear parent function $f\left(x\right)=x$ is graphed on the grid. Which graph best represents $g\left(x\right)=-f\left(x\right)-3$ ?

a)

b)

c)

d)

18.

Linear parent function $f\left(x\right)=x$ is graphed on the grid. Which graph best represents $g\left(x\right)=-\frac{1}{3}f\left(x\right)$ ?

a)

b)

c)

d)

19.

Which transformation will occur if $f\left(x\right)=x$ is replaced with $-f\left(x\right)-4$ ?

a)

Vertical translation up and reflection

b)

Vertical translation down

c)

Vertical stretch (more steep) and vertical translation down

d)

Reflection and vertical translation down

20.

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

21.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

Transformations of Linear Functions

Total questions: 21

Worksheet time: 21mins

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