Algebra and Trigonometry: Transformations of Functions

Question 1

What is the equation for the function shown in the graph?

Accepted Answer

y=\left(x-4\right)^2

Question 2

What is the equation for the function shown in the graph?

Accepted Answer

h\left(x\right)=\left(x+2\right)^3+1

Question 3

If g\left(x\right)=f\left(2x+1\right) and f\left(x\right)=3x+7, g\left(x\right)=?

Accepted Answer

6x+10

Question 4

Which of the equations is found using the general form for a horizontal stretch of the functionf\left(x\right)=x^5

Accepted Answer

h\left(x\right)=\left(\frac{1}{3}x\right)^5

Question 5

Which of the transformations could change the y-intercept of a function?

Accepted Answer

Vertical Compression, Vertical Stretch, Horizontal Translation

Question 6

If f\left(x\right)=x^2 and g\left(x\right)=f\left(2x+1\right), g\left(x\right)=?

Accepted Answer

4x^2+4x+1

Question 7

What is the equation for the reflection of f\left(x\right)=x^5+x^4 over the x-axis?

Accepted Answer

j\left(x\right)=-x^5-x^4

Question 8

Which does "horizontal" refer to?

Accepted Answer

The input

Question 9

If f\left(x\right)=\left|x\right| and g\left(x\right)=-\left|x+1\right|, what transformations have taken place?

Accepted Answer

Reflection over the x-axis, Horizontal Translation

Question 10

If f\left(x\right)=\sqrt{x}, and g\left(x\right)=2\sqrt{x+1}, what transformations have taken place?

Accepted Answer

Vertical Stretch, Horizontal Translation

Question 11

If f\left(x\right)=x-1 and g\left(x\right)=4\cdot f\left(x\right)-3, g\left(x\right)=?

Accepted Answer

4x-7

Questions 11