Transformations of Polynomial Functions Quiz

Write g(x) in terms of f(x) =  $x^3$ after performing a vertical stretch of by a factor of 4 followed by a translation of 3 units up.

•  $g\left(x\right)=4x^3+3$  

•  $g\left(x\right)=\frac{1}{4}x^3+3$  

•  $g\left(x\right)=4x^3-3$  

•  $g\left(x\right)=\frac{1}{4}x^3-3$  

Identify the parent function for $g\left(x\right)=\left(x+7\right)^2-3$  

 and describe what transformation of the parent function it represents.

• The parent function is the quadratic function  $f\left(x\right)=x^2$  .
   $g\left(x\right)=\left(x+7\right)^2-3$  represents a horizontal translation of 7 to the right and a vertical translation of the parent function 3 units up.
  

• The parent function is the quadratic function  $f\left(x\right)=x^2$  . $g\left(x\right)=\left(x+7\right)^2-3$  represents a horizontal translation of 7 to the left and a vertical translation of the parent function 3 units up.

• The parent function is the quadratic function  $f\left(x\right)=x^2$  . $g\left(x\right)=\left(x+7\right)^2-3$  represents a horizontal translation of 7 to the left and a vertical translation of the parent function 3 units down.

• The parent function is the quadratic function  $f\left(x\right)=x^2$  . $g\left(x\right)=\left(x+7\right)^2-3$  represents a horizontal translation of 7 to the right and a vertical translation of the parent function 3 units down.

Which of the following polynomial functions could have the graph shown?

• $h\left(x\right)=x\left(x+1\right)\left(x-2\right)$

• $h\left(x\right)=x^2\left(x+1\right)\left(x-2\right)$

• $h\left(x\right)=x\left(x-1\right)\left(x+2\right)$

• $h\left(x\right)=\left(x+1\right)^2\left(x-2\right)$

The graph of the polynomial function $f\left(x\right)$  is shown. What are the zeros of  $f\left(x\right)$ ? (Assume that the zeros are integers and that the graph does not cross the x-axis at places other than those shown.)

• x = 2, x = 0, and x = -1

• x = 2 and x = -1

• x = -2, and x = 1

• x = -2, x = 0 and x = 1

Which of the following polynomial functions could have the graph shown?

• $g\left(x\right)=-x^3$

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

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

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

 $f\left(x\right)=7x\ -\ 5$  

What is the inverse of the function

•  $f^{-1}\left(x\right)=\frac{x+5}{7}$  

•  $f^{-1}\left(x\right)=\frac{x-5}{7}$  

•  $f^{-1}\left(x\right)=5x+7$  

•  $f^{-1}\left(x\right)=\frac{x+7}{5}$  

Which is a graph of an even degree function with a negative leading coefficient?

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Identify global and/or local maximums and minimums for the following graph.

• 1 global maximum and1global minimum

• 1 local maximum and 1 local minimum

• 1 global maximum and 1 local minimum

• No global or local maximum or minimums

 $g\left(x\right)=x^2\left(x-4\right)$  

Identify the number of turning points and the x-intercepts in this function.

Note: Please use your Desmos graphing calculator to graph this and decide the correct answer.

• 1 turning point; x = 4

• 3 turning points; x = 0 and x = 4

• 2 turning points; x = 0 and x = 4

• 2 turning points; x = 0 and x = -4

To create an open-top box out of a sheet of cardboard that is 6 inches long and 4 inches wide, you make a square flap of side length x inches in each corner by cutting along one of the flap’s sides and folding along the other. To the nearest tenth, find the value of x that maximizes the volume of the box.

Use your Desmos graphing calculator to find this value.

• 0.8 inches

• 8.5 inches

• 1.6 inches

• 17.0 inches