Domain, Range, Zeroes, Intercepts, Functions

Review for FUNCTIONS TEST

by Denae McNeily

​Question type 1: KEY FEATURES

​Determining domain and range of a function

​Determining vertex point of a parabola function

​Determining x-intercept of a function

​Determining y-intercept of a function

​Determining the maximum or minimum point for a function (specifically parabola)

​Determining the slope of a function OR on a certain interval of a function

​

​

​The following questions are SAMPLES to practice for the test

Multiple Choice

What is another name for the x-intercepts of a quadratic?

• y-intercept
• Zeros
• x-axis
• They don't have another name

​Explanation:

​x-intercepts of a parabola are referred to as:

​

​ x-intercepts

​ zeros

​ roots

​ solutions

Multiple Choice

What is the x-intercept for the given graph?

• 1
• -2
• 2
• 1/2

Multiple Choice

What is the y-intercept for the given graph?

• 1
• -2
• 2
• 1/2

Explanation:​

x-intercept is where a graph (any graph) crosses the x-axis

y-intercept is where a graph (any graph) crosses the y-axis.

There can be one or more than one intercept for the graph of a function​

Multiple Choice

Determine the equation for the line

• $$y=\frac{2}{3}x+3$$

• $$y=\frac{2}{3}x+2$$

• $$y=\frac{2}{3}x-2$$

• $$y=-2x+\frac{2}{3}$$

​To write the equation:

​y = mx + b

​y =(2/3)x - 2

​

​

Multiple Choice

Which function has a maximum at (2, 0)?

Multiple Choice

Determine the domain and range of the function

• Domain: All real numbers, Range: All real numbers

• Domain: x ≥ -4, Range: All real numbers

• Domain: All real numbers, Range: y ≥ -4

• Domain: -1 ≤ x ≤ 5, Range: y ≥ -4

Multiple Choice

What is the equation of the axis of symmetry?

• y = 0

• x = 0

• x = 3

• x = -3

Multiple Choice

Which function has a range y ≥ -4?

• None of the above

Multiple Choice

What are the zeros?

• 0 and 2

• -4 and 0

• 2 and 3

• 0 and 4

Multiple Choice

What is the vertex for the parabola? $$f(x)=4(x-2)^2+3$$  

• (-2, 3)

• (2, -3)

• (4, 3)

• (2, 3)

Multiple Choice

Does the parabola open up or down? $$f(x)=4(x-2)^2+3$$  

• up

• down

​Remember:

​

​USE the graphing calculator!

​If the question asks for the VERTEX of a parabola, graph it and look for the vertex.

​

​If the question wants to know if the graph would be "down or up" graph it!!!

​

​Don't forget you can GRAPH and ANSWER many questions.

​Question type 2: RATE of CHANGE, i.e. SLOPE

Multiple Choice

Find the rate of change.

• -2 minutes per gallon
• -20 minutes per gallon
• -2 gallons per minute
• -20 gallons per minute

Multiple Choice

What is the rate of change in the graph?

• -6
• -1/6
• 2
• -4

Multiple Choice

• Taylor can write 6 words per minute
• Taylor can write 25 words per minute
• Taylor can write 50 words per minute
• Taylor can write 150 words per minute

Multiple Choice

At what rate did the rain fall?

• 2 cm per hour
• ¹/₄ cm per hour
• ¹/₂ cm per hour
• 4 cm per hour

Multiple Choice

What is the slope of

• $$\frac{2}{3}$$

• $$-\frac{2}{3}$$

• $$\frac{3}{2}$$

• $$-\frac{3}{2}$$

Multiple Choice

Which statement below accurately represents the graph?

• $100 is earned for each hour worked

• $100 is earned for every 2 hours worked

• $500 is earned for every 8 hours worked

• $150 is earned for every 3 hours worked

​QUESTION TYPE 3: Operations of functions

​You must know how to complete ALL the operations of functions:

addition

​subtraction

​multiplication

​division

​

​INCLUDING: evaluating

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

• x²-2x+6
• -x²+2x+4
• -x²-2x-6
• x²-2x-4

Multiple Choice

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x). 

• x²+x+9
• x²-x+9
• x²-x
• x²-x+18

Multiple Choice

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

• x²-2x+6
• -x²+2x+4
• -x²-2x-6
• x²-2x-4

Multiple Choice

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x). 

• 14x-10
• -8x+2
• 2x+2
• 2x-2

Multiple Choice

f(x) = 4x + 1 and g(x) = 4x - 3
Find f(x) * g(x)

• 16x² + 8x - 3
• 16x² - 8x + 3
• 16x² - 8x - 3
• 16x² - 16x - 3

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

​Question Type 4: TRANSFORMATIONS of FUNCTIONS

You must know how to shift/translate/slide a function up, down, left and right

UP: f(x) + h DOWN:​ f(x) - h ​LEFT: f(x + h) RIGHT: f(x - h)

​

You must know how to reflect a function

​ X-axis reflection (upside-down). -f(x)

​ Y-axis reflection (left-to-right). f(-x)

​

​You must know how to re-size a function

​ multiply number to function: 5f(x) or f(1/2x)

Multiple Choice

f(x) = 5x² + 2

• Stretch of 5
  Up 2
• Shrink of 5
  Up 2
• Stretch of 5
  Down 2
• Shrink of 5
  Down 2

Multiple Choice

. 
If the blue is f(x)=x^2, then the red must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Multiple Choice

. 
If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

Multiple Choice

g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated to the left one and down five.
• f(x) has been translated to the right one and down five.
• f(x) has been translated to the left one and up five.
• f(x) has been translated to the right one and up five.

Multiple Choice

Identify the transformation from the graph of f(x)=x² to the graph g(x)= (x+5)²

• shifted up five units

• shifted down five units

• shifted left 5 units

• shifted right 5 units

Multiple Choice

What is the rule for the transformation of g(x) in terms of f(x)?

• g(x)=f(x)+5
• f(x)=g(x)+5
• g(x)=f(x)-5
• f(x)=g(x)-5

Multiple Choice

What is the rule for the transformation of g(x) in terms of f(x)?

• g(x)=f(x)+4
• f(x)=g(x)+4
• g(x)=f(x)-4
• f(x)=g(x)-4

Multiple Choice

Describe the transformation: $$f\left(x\right)=\frac{1}{3}x^2+2$$  

• Vertical compression by a factor of of 1/3
  Up 2

• Vertical stretch by a factor of 1/3
  Up 2

• reflection over the x-axis
  Up 2

• Vertical compression by a factor of of 1/3

  Right 2

Multiple Choice

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2
• x² - 2
• (x + 2)²
• (x - 2)²

Multiple Choice

  The blue function is the original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Multiple Choice

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

• Reflect over y-axis
  Shifted down 10 units
  Shifted left 6 units
• Reflect over x-axis
  Shifted up 10 units
  Shifted left 6 units
• Reflect over y-axis
  Shifted up 10 units
  Shifted right 6 units
• Reflect over x-axis
  Shifted down 10 units
  Shifted left 6 units

Multiple Choice

Identify the transformation from the graph of f(x)=2^x to the graph g(x)=2^x + 4

• shifted up four units
• shifted down four units
• shifted left four units
• shifted right four units

Multiple Choice

Identify the transformation from the graph of f(x)=x² to the graph g(x)= x² - 5

• shifted up five units
• shifted down five units
• shifted left five units
• shifted right five units

​Question Type 5: INVERSE of a function

​You have to know how to write the inverse of a function

Multiple Choice

What does it mean to find the inverse of a function?

• the x's and y's are switched
• the x's and y's are divided by 2
• the x's and y's are made negative
• the x's and y's are the same

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)
• (-4, -1) and (-6, -4)
• (-1, -4) and (-4, -6)
• (4, 1) and (6, 4)

Multiple Choice

If f(x)=3x, what is f^-1(x)?

• x/3

• 3x²

• 3x + 3x

• 3x^-1

Multiple Choice

Find the inverse of f(x) = -4x - 12

• f^-1(x) = 4x - 3
• f^-1(x) = -1/4x - 3
• f^-1(x) = 1/4x + 3
• f^-1(x) = -4x - 3

Multiple Choice

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 4x + 7
• f^-1(x) = -4x + 28
• f^-1(x) = -4x - 7
• f^-1(x) = 4x + 28

Multiple Choice

Which is f ^-1(x)?

• f ^-1(x) = 5x + 3

• f ^-1(x) = 5x - 3

• f ^-1(x) = 5x - 15

• f ^-1(x) = 1/5(x) + 3/5

Multiple Choice

FInd the inverse of the function. $$f\left(x\right)=\frac{3x-15}{2}$$  

• $$f^{-1}\left(x\right)=-x-5$$  

• $$f^{-1}\left(x\right)=3x+5$$  

• $$f^{-1}\left(x\right)=\frac{15+2x}{3}$$  

• $$f^{-1}\left(x\right)=\frac{2}{3}x-\frac{19}{3}$$  

Multiple Choice

Find the inverse of the function. $$f\left(n\right)=-4-\frac{2}{5}n$$  

• $$f^{-1}\left(n\right)=\frac{-6-5n}{2}$$  

• $$f^{-1}\left(n\right)=3n-4$$  

• $$f^{-1}\left(n\right)=-\frac{5}{2}n-10$$  

• $$f^{-1}\left(n\right)=\frac{-2n-4}{5}$$  

Multiple Choice

What is the inverse of the function
f(x) = 2x + 4   ?

• f^-1(x) = 4(x -2)
• f^-1(x) = (x-4)/2
• f^-1(x) = x/2 - 4
• f^-1(x) = x/4 + 2

​Question type: Different WAYS to represent functions:

​To represent a function you can:

​1. Write the equation in different forms

​ 3x + y = 10 is the same as y = -3x + 10​

​2. Give the ordered pairs 3. Give the graph

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​4. Give a written description

​add 10 to the product of the input values and -3