Domain and Range Quiz and End Behavior

Describe the end behavior of the function shown: y=log₂(x+1)

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Answer explanation

What is the domain and range of the function y=2^x ? Use the graph to help!

• Domain: (−∞,∞)

  Range: (0,∞)

• Domain: (−∞,∞)

  Range: (1,∞)

• Domain: (−2,∞)

  Range: (0,∞)

• Domain: (−∞,∞)

  Range: (−∞,0)

• The end behavior of the graph is x →∞, f(x) →⁻∞ and x →⁻∞, f(x) →⁻∞

• The end behavior of the graph is x →∞, f(x) →∞ and x→⁻∞, f(x) →∞

• The end behavior of the graph is x →∞, f(x) →∞ and x→⁻∞, f(x) →2

• The end behavior of the graph is x →∞, f(x) →2 and x→⁻∞, f(x) →∞

This is an example of....

• an increasing exponential function

• a decreasing exponential function

• an increasing linear function

• none of the above

Select TWO correct answers.

Domain

​ (a)  

Range

​ (b)  

• The domain of the function is {0,1,2,3,4,5}

• The range of the function {0,96,192,288,384,480}

• The domain of the function is all real numbers

• The domain of the function {0,96,192,288,384,480}

• The range of the function {0,1,2,3,4,5}

• The range of the function is all real numbers.

The mapping below represents all of the points on the graph of function f.

What is the domain and range of f.

Domain: ​ (a)  

Range: ​ (b)  

• {-5, -3, 0, 2, 4}

• {-1, 0, 1, 2, 3}

• {5}

• {-5, -3, -1, 0, 2, 3, 4}

A student borrowed $480 from a friend. He agreed to make monthly payments of $96 with no interest until the loan balance was paid off. The function shown models this situation, where f(x) represents the remaining loan balance in dollars after the student has made x monthly payments. Which statements are true about the domain and range of the function for this situation? Select the correct answers.

• D: {0, 1, 2, 3, 4, 5}

• R: {0, 96, 192, 288, 384, 480}

• D: all real numbers

• R: {0, 1, 2, 3, 4, 5}

• {0, 96, 192, 288, 384, 480}

• D: {0, 96, 192, 288, 384, 480}

• R: all real numbers

Answer explanation

Domain - x values

Range - y values

Real-world examples = apply common sense and judgements

The graph shown has a domain of​ (a)   .

It has a range of (b)   ​ (c)   (d)   . ​

• ARN

• y

• >

• G

• x

• <

• E

• B

• A

• H

Describe the transformations, asymptote, domain, and range for the following function: f(x)=-3(2)^(x-4)+6

• Transformation: Vertically stretched factor 3, translated right 4 and down 6. 
  Horizontal Asymptote at y = - 6 
  Domain: (-∞,∞)   Range: (-∞,6)

• Transformation: Reflection over x-axis, vertically stretched factor 3, translated right 4 and up 6. 
  Horizontal Asymptote at y = 6 
  Domain: (-∞,∞)   Range: (-∞,6)

• Transformation: Reflection over x-axis, vertically stretched factor 1/3, translated Left 4 and up 6. 
  Horizontal Asymptote at y = 6 
  Domain: (-∞,∞)   Range: (6,-∞)

• Transformation: Reflection over x-axis, vertically stretched factor 1/3, translated Left 4 and Down 6. 
  Horizontal Asymptote at y =6
  Domain: (-∞,∞)   Range: (6,-∞)

What is the domain of this graph?