Functions Unit Test Review

Functions Unit Test Review

Final Review for Functions Test!

Functions - Words to know!

• Function: A relationship in which every input has exactly one output.

• Input: all x-values, domain, independent variable

• Output: all y-values, range, dependent variable

Multiple Choice

Which of the following is another name for Input?

• Domain

• Range

• y-value

Multiple Choice

Which of the following is another name for output?

• Domain

• Independent Variable

• y-value

• x-value

Multiple Choice

Function or Not a Function?

• Function

• Not a Function

Multiple Choice

Function or Not a Function?

• Function

• Not a Function

Multiple Choice

What is the domain of the relation given?

• {5, 2, -7, 1, 0, 3, 4, -4}

• {2, 1, 3, -4}

• {2, -7, 0. 4}

• {5, -7, 0, 4}

Multiple Choice

What is the range of the function $y\ =\ 2x\ +1$ when the domain given is { -2, 0, 2}?

• {-3, 1, 5}

• {5, 1}

• {3, 1, 5}

• {3, 1, -5)

Slope from a Graph

• Slope is written as a fraction in simplest form

• Variable for slope: m

• Slope is written as a ratio of the rise over the run

Slope Formula

Used to find the slope between any two points (x₁, y₁) and (x₂, y₂).

Multiple Choice

What is the slope of the line between points (4, -9) and (4, 1)?

• 0

• undefined

• 13/5

• -1

Multiple Choice

Find the slope from the table.

• -2

• -1/2

• 19/4

• 1/2

Multiple Choice

What is the slope of the line between points (7, 3) and (6, -2)?

• -1/2

• -1/5

• 5

• -3

Multiple Choice

Find the slope of the graph.

• 4/7

• -4/7

• -7/4

• 7/4

Multiple Choice

Find the slope of the graph.

• 1

• 0

• undefined

• -1

Slope Application

• When given a table or a graph, find the rate of change by using the slope formula.

Multiple Choice

Using the table, find the rate of change from 2004 to 2010.

• $0.11

• $8.60

• $0.70

Multiple Choice

Using the graph, what is the rate of change in miles from September 3rd to September 6th?

• 6 miles

• 0.67 miles

• 2 miles

• 1.5 miles

Slope-Intercept Form

• Linear equations are frequently written in slope intercept form

• m = slope, the rate of change of the function

• b = y-intercept, where the graph would cross the y-axis

Multiple Choice

What is the slope of the following equation? $y=-2x+4$  

• 2

• -2

• 4

• -4

Multiple Choice

What is the y-intercept of the following equation? $y=\frac{3}{2}x-4$  

• 3/2

• -3/2

• 4

• -4

Multiple Choice

Which equation has a y-intercept of 5? 

• y = 2x  - 5

• y = 5x

• y = 2x + 5

• y = 5x - 5

Multiple Choice

Which equation has a slope of 1?

• y = 2x + 1

• y = 1 - 2x

• y = 1

• y = x + 3

Multiple Choice

Which of the following equations matches the graph?

• $y\ =\ \frac{2}{3}x$

• $y\ =\ \frac{2}{3}x\ +1$

• $y\ =\ -\frac{3}{2}x-1$

• $y\ =\ -\frac{2}{3}x-1$

Multiple Choice

Which of the following equations matches the graph?

•  $y\ =\ 5x\ -2$ 

•  $y\ =\ -\frac{1}{5}x\ +2$ 

•  $y\ =\ 5x\ +\ 2$ 

•  $y\ =\ \frac{1}{5}x\ -2$ 

Multiple Choice

Which of the following equations matches the graph?

•  $y\ =\ -\frac{1}{2}x\ +1$ 

•  $y\ =\ -2x$ 

•  $y\ =\ -\frac{1}{2}x$ 

•  $y\ =\ 2x\ +1$ 

Multiple Choice

Which of the following equations matches the graph?

•  $y\ =\ \frac{2}{7}x\ +3$ 

•  $y\ =\ -\frac{2}{7}x\ +2$ 

•  $y\ =\ \frac{7}{2}x-3$ 

•  $y\ =\ -\frac{7}{2}x\ -3$ 

Standard Form

• Sometimes equations are written in Ax + By = C format.

• In order to graph these functions, we must put them in slope-intercept form (y = mx + b)!

Multiple Choice

What is 2x + y = 4 in slope-intercept form?

• y = 2x + 4

• y = -2x + 4

• y = 4x + 2

• y = 2x - 4

Multiple Choice

What is 4x + 2y = 6 in slope-intercept form?

• y = 4x + 6

• y = -2x + 6

• y = -2x + 3

• y = 2x - 4

Multiple Choice

What is -3x + 6y = 6 in slope-intercept form?

• $y\ =\ -\frac{1}{2}x\ +\ 6$

• $y\ =\ \frac{1}{2}x\ +\ 1$
  

• $y\ =\ 2x\ +\ 6$

• $y\ =\ -2x\ +\ 1$
  

Multiple Choice

Which equations has a slope of 4 and a y-intercept of 1? Hint: You must CONVERT to y = mx + b.

• 4x + y = -1

• x + y = 4

• -4x + y = 1

• x + 4y = 4

Linear vs Nonlinear

• Linear Functions: functions that form a straight line on a graph and have a constant slope

• Nonlinear Functions: functions that DO NOT form a straight line (often a curve) and do not have a consistent slope. Equations that have any exponent other than 1, or cannot be put in slope-intercept form are nonlinear.

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• linear

• nonlinear

Multiple Choice

The taxi company charges $0.75 per mile driven in addition to a flat fee of $3.00. Write an equation to represent the total cost for a taxi cab trip. What is the rate of change?

• $0.75

• $3.00

• $4.00

• $0.25

Multiple Choice

The taxi company charges $0.75 per mile driven in addition to a flat fee of $3.00. Write an equation to represent the total cost for a taxi cab trip. What is the initial value?

• $0.75

• $3.00

• $4.00

• $0.25

Multiple Choice

The taxi company charges $0.75 per mile driven in addition to a flat fee of $3.00. Write an equation to represent the total cost for a taxi cab trip. What is the independent variable?

• Flat fee

• Number of Miles

• Total Cost

Multiple Choice

The taxi company charges $0.75 per mile driven in addition to a flat fee of $3.00. Write an equation to represent the total cost for a taxi cab trip. What is the dependent variable?

• Flat fee

• Number of Miles

• Total Cost