Exploring Intro to Functions and Rational Expressions

The video introduces the concept of functions, explaining that they are relationships where each input has a single output. It covers the domain and range of functions, how to identify functions using tables and the vertical line test, and introduces function notation. The video also includes examples and exercises to help students understand these concepts.

What is the term used to describe the set of all possible input values for a function?

• Variable

• Output

• Domain

• Range

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In a function, what must be true about the relationship between inputs and outputs?

• Each input can have multiple outputs.

• Each input must be equal to its output.

• Each input can have only one output.

• Each output can have multiple inputs.

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Which of the following sets of ordered pairs represents a function?

• (0, 1), (1, 2), (2, 3), (3, 4)

• (-3, 4), (0, 8), (1, 6), (7, 11)

• (1, 2), (2, 3), (1, 4), (3, 5)

• (2, 3), (2, 4), (3, 5), (4, 6)

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Why does the input value of 1 mapping to both 0 and 15 make a relationship not a function?

• Because the outputs must be the same.

• Because 1 is not a valid input.

• Because an input can only map to one output.

• Because 0 and 15 are not valid outputs.

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What is the purpose of the vertical line test?

• To find the slope of a graph.

• To determine if a graph is linear.

• To identify the range of a function.

• To check if a graph represents a function.

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If a vertical line intersects a graph at more than one point, what does this indicate?

• The graph is not a function.

• The graph has no range.

• The graph is a function.

• The graph is linear.

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What is the benefit of using function notation?

• It simplifies the process of solving equations.

• It makes the function more complex.

• It allows for easy substitution of input values to get output values.

• It eliminates the need for variables.

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In function notation, what does f(2) = 13 mean?

• The function f at x equals 2 gives an output of 13.

• The function f is equal to 13 times 2.

• The function f at x equals 13 gives an output of 2.

• The function f is equal to 2 times 13.

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How would you write the function y = 3x + 7 in function notation?

• 3x + 7 = f(x)

• f(y) = 3x + 7

• y = f(x) + 7

• f(x) = 3x + 7

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If k(t) = t^2 - t, what is k(-4)?

• 24

• 16

• 20

• 12

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