FUNCTION GRAPHs 1

FUNCTION GRAPHs 1

Absolute Value, Rational, Root, Step (Greatest Integer), and Piecewise

ABSOLUTE VALUE FUNCTION

• V-Shaped graph with absolute value symbols

•  $f\left(x\right)=2\left|x\right|-1$  

•  $y=\left|x\right|+3$  

Multiple Choice

Which absolute value function is graphed?

(Hint: Use a graphing calculator to answer)

• f(x) = 2|x + 2| -4

• f(x) = 2|x - 4| + 2

• f(x) = |x + 2| - 4

• f(x) = -2|x - 4|

Multiple Choice

Which function is an absolute value function?

• $f\left(x\right)=x+7$

• $f\left(x\right)=x^2-2x+3$

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

• $f\left(x\right)=7x$

Multiple Choice

What is the vertex of the function: y= 4|x|+1

(Hint: Graph the function)

• (0,1)

• (4,1)

• (-4,1)

• (4,-1)

RATIONAL FUNCTION

• graphs are often discontinuous.

• A vertical line with equation x = a is called a vertical asymptote of the graph of the function.

• function is fractional with variable in the denominator

Multiple Choice

What is the equation of the rational function graphed?

(Hint: Use a graphing calculator)

Multiple Choice

What is the equation of the graph? (Hint: Use the graphing calculator)

Multiple Choice

What are the asymptotes?

(asymptote is a line the graph approaches but never touches)

• x=1, x= 2, y =1, y= 2

• x= 2, x=-2, y = 1

• x=2 y =-1

• x=1 y =2, y =-2

RADICAL (SQUARE ROOT) FUNCTION

• has a square root in it

Multiple Choice

Which of the following is a radical function?

• $f\left(x\right)=5x-1$

• $f\left(x\right)=x^2+3$

• $f\left(x\right)=\sqrt{x}-1$

• $f\left(x\right)=-3\left|x\right|+6$

Multiple Choice

• A

• B

• C

• D

CUBE ROOT FUNCTION

• has a cube root in it

• looks like a snake

Multiple Choice

Match the equation with the graph

• $y=\sqrt[3]{x-3}+5$

• $y=\sqrt[3]{x-3}-5$

• $y=\sqrt[3]{x+3}+5$

• $y=\sqrt[3]{x+3}-5$

Multiple Choice

What is the center point of the function?

• (5,-3)

• (5,3)

• (-5,-3)

• (-5,3)

Multiple Choice

What kind of function is represented by the graph?

• Cube Root Function

• Cubic Function

• Polynomial Function

• Square Root Function

STEP (or GREATEST INTEGER) FUNCTION

• graph looks like steps

• has [  ] in it 
  

• f(x) = [[x + 1]]

Multiple Choice

Identify the Step Function or Greatest Function.

•  $f\left(x\right)=2x^2+1$  

•  $f\left(x\right)=3x-1$  

•  $f\left(x\right)=2\left[x+1\right]\$  

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

Multiple Choice

Evaluate f(2.7)

• 2

• 3

• 2.5

• 2.7

Multiple Choice

1. What is this type of function called?

• Discrete Function

• Segment Function

• Step Function

• Jump Function

• Linear

PIECEWISE FUNCTION

• graph appears to be in pieces or sections

Multiple Choice

Which one is the correct equation of the piecewise function?

Multiple Choice

Find f(2)

• f(2) = 0

• f(2) = 1

• f(2) = 3

• f(2) = 4

Multiple Choice

What is the DOMAIN of the function?

• (-∞, +∞)

• (-∞, 4]

• (-∞, 4)

• [0, 4]