Unit 5 Lesson 6

Determine which of the following functions could be represented by the graph.

(select all that apply)

Answer explanation

Could be f(x) because:

- vertex is negative: (-3, -2)

- opens upwards

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Could be m(x) because:

- has two negative roots

- roots at x= -4 and x= -2

- opens upwards

Which function is modeled by the function?

• f(x) = -x + 4

• f(x) = 3x

• f(x) = 2x + 1

• f(x) = x - 3

• f(x) = x + 3

Answer explanation

Try to match an input for x and output for y

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Using input of x = 0 only works for one function option

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f(0) = 2(0) + 1 = 1

Consider the functions f(x) and g(x). Determine the type of function each models.

(linear, quadratic, neither)

Answer explanation

F(x) is linear

G(x) is quadratic

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There is more than one way to know g(x) is quadratic

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1) Look at table and see that y-values repeat

2) Look at table and find constant second difference

3) Plot the points in Desmos

Consider the functions f(x) and g(x). Determine the y-intercept for each function.

Answer explanation

Y-intercept is when x = 0 on a graph or table

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F(x) has y-intercept of -5

G(x) has y-intercept of 9

Consider the function f(x). Find the R.O.C. from [0, 2] for f(x).

Mathematical Equivalence

ON

Consider the function f(x). Write an equation for the graph.

Answer explanation

Many ways to write answer

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y = -5 + 3x

y = 3x - 5

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f(x) = -5 + 3x

f(x) = 3x - 5

What type of function (Linear or Quadratic) would best describe the squeegee’s height as a function of time? Explain your thinking.

Answer explanation

More than one way to answer

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1) Find common first or second difference

2) Plot graph in Desmos

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Plot supports quadratic function

The table of values for two functions is shown. Determine if the functions are linear or exponential.

Answer explanation

F(x) is linear since it has a constant first difference

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G(x) is quadratic since it has a constant second difference

G(x) graph also supports pattern for quadratic function

What equation models function g(x)?

• g(x) = 2x

• g(x) = -2x

• g(x) = x²

• g(x) = 2x²

Answer explanation

More than one way to answer question

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1) match input and output values

2) use regression in Desmos

Consider the functions f(x) and g(x). Determine the x-intercept and y-intercept values for each function.