Quiz 3.1 and 3.2 Graphing and attributes of a function

What is true about the function given below? $f\left(x\right)=-\left(x-2\right)^2+4$  

Select all the correct answers.

• The range is  $y\le4$  

• The y - intercept is (0, 4)

• The x-intercepts are (0,0) and (4,0)

• It is a quadratic function!

• The minimum point is (2,4)

Which function(s) have the same domain and range?

• $f\left(x\right)=\left(x+3\right)^2-5$

• $h\left(x\right)=-\left|x+3\right|-5$

• $z\left(x\right)=\left|x+2\right|+5$

• $g\left(x\right)=\left(x-8\right)^2-5$

• $h\left(x\right)=x^4-5$

What is the x-intercept for the function? Show your work by hand on paper!!
 ( a picture of a graph will not be counted as work)
Then type in your answer. (Only type the number or the point(use parenthesis () for point), but don't use spaces)
 $g\left(x\right)=-\frac{1}{7}x+4$  

(a)  

 $f\left(x\right)=-\left|x-1\right|+3$  

What is the x-intercept(s) and y-intercept for t he problem above? Select the correct answers.

• (-2,0)

• (0, -2)

• (0, 2)

• (4,0)

• (0, 4)

Given: $f\left(x\right)=x^3-6x^2+9x+1$  

Describe the name of the function and its minimum or maximum number!

• It is a cubic function with a maximum point of (3,1)

• It is a cubic function with a minimum point of (1,5)

• It is a cubic function with a minimum point of (3,1)

• It is a cubic function with a maximum point of (0,1)

What is the horizontal and vertical shift for: $f\left(x\right)=-\sqrt{x-1}+5$  

• Horizontal Shift: 5 units up
  Vertical Shift: 1 unit right

• Horizontal Shift: 5 units up
  Vertical Shift: 1 unit left

• Horizontal Shift: 5 units down
  Vertical Shift: 1 unit right

• Horizontal Shift: 5 units down
  Vertical Shift: 1 unit left

What is the domain and range for the radical function below?
 $f\left(x\right)=\sqrt{x+2}-3$   

Select the correct answers.

•  $x\ge-2$  

•  $x\le-2$  

•  $y\ge-3$  

•  $y\le-3$  

Find the x-intercept(s) and the y-intercept.

Given: $g\left(x\right)=2x^2-8$  

Show your work by hand on paper!! 

Then select the correct answer.

(A picture of a graph will not be counted as work)

• The x-intercept(2,0) and y-intercept (0,-8)

• The x-intercepts are (0,2) and (0,-2) y-intercept(0,-8)

• The x-intercept is (2,0) and y-intercept (-8,0)

• The x-intercepts are (2,0) and (-2,0) y-intercept(0,-8)

Graph: $f\left(x\right)=\left(x+3\right)^2-7$  

Then determine what the domain and range is.

• Domain: All real numbers
  Range:  $y\le-7$  

• Domain:  $x\ge-3$  
  Range:  $y\ge-7$  

• Domain: All real numbers
  Range:  $y\ge-7$  

• Domain:  $x\le-3$  
  Range:  $y\le-7$  

What is true about the polynomial function given in the picture? Select all the correct answers.

• The maximum point is (0,4)

• The minimum point is (2.5, -4.5)

• The range is $y\ge-4.5$

• The y-intercept is (4,0)

• The domain is all real numbers.