Free Printable Transformations

1.

Given $f\left(x-3\right)+5$ . What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

2.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

a)

-f(x)

b)

f(-x)

c)

f^-1(x)

d)

f(2x)

3.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

$g\left(x\right)=x^3+1$

b)

$g\left(x\right)=x^3-1$

c)

$g\left(x\right)=\left(x-1\right)^3$

d)

$g\left(x\right)=\left(x+1\right)^3$

4.

Identify the transformation from the graph of $f\left(x\right)=\sin\left(x\right)$ to the graph of $g(x)=-\sin(x+5)$

a)

shifted up five units

reflection in x-axis

b)

shifted down five units

reflection in x-axis

c)

shifted left 5 units

reflection x-axis

d)

shifted right 5 units

reflection x-axis

5.

$3f\left(x-2\right)$ Identify the transformations.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical shrink by a factor of 3

d)

horizontal shift to the left 2 and vertical shrink by a factor of 3

6.

If the yellow curve has equation $f(x)=x^2$

a)

Then the blue curve is $f(x)=x^2-c$

b)

Then the blue curve is $f(x)=(x+c)^2$

c)

Then the blue curve is $f(x)=(x-c)^2$

d)

Then the blue curve is $f(x)=x2+c$

7.

The original function has equation $f(x)=\frac{2}{3}\sqrt{x-7}$

State the transformations given the new function

a)

Vertical Compression of ⅔
Right 7

b)

Horizontal Compression of ⅔
Left 7

c)

Left ⅔

Vertical stretch of 7

d)

Right ⅔

Horizontal stretch of 7

8.

If the original function is f(x) then state the transformation that takes $f\left(x\right)$ to $g(x)=|-x+3|$

a)

Left 3 then Reflect over y-axis

b)

Right 3 then Reflect over y-axis

c)

Left 3 then Reflect over x-axis

d)

Right 3 then Reflect over x-axis

9.

$f\left(x\right)$ is transformed so that it maps onto $g\left(x\right)$ . Which equation would correctly represent $g\left(x\right)$ ?

a)

$g(x)=2f(x)$

b)

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

c)

$g(x)=f(x)+2$

d)

$g(x)=f(x+2)$

10.

Describe the transformation of $y=f\left(x\right)$ to the new function $y=f\left(\frac{1}{5}x\right)$

a)

Horizontal compression by a factor of 1/5

b)

Vertical stretch be a factor of 5

c)

Vertically compression by a factor of 1/5

d)

Horizontal stretch by a factor of 5

Transformations

Total questions: 10

Worksheet time: 20mins

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