Linear Functions Review

What is the domain?

• [-5,5]

• [4,10]

• {-5, -2, 1, 5}

• {4, 10, 11}

Answer explanation

Since you can count four distinct coordinate points, this is a discrete function. Set notation using squiggly brackets will be used to describe the x-values.

What is the range?

• {10, 11, 4, 10}

• [4,10]

• [-5,5]

• {4, 10, 11}

Answer explanation

Repeated y-values should only be written once. Since this is a discrete function, set notation will be used.

Which statement best describes the table shown?

• A function that is one-to-one.

• This set of coordinate points is not a function.

• It is a function, but not a one-to-one function.

Answer explanation

None of the x-values are repeated, making this table a function. But since the y-value of 10 is used twice, it cannot be considered a one-to-one function.

Mark which of the following relations are functions:

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Answer explanation

The graph fails the Vertical Line Test, making it not a function.

The map diagram shows that -4 goes to two y-values, 12 and 15.

The other two options do not have any repeating x-values.

What is the value of f(-2) for the function f(x)=4x+10.

• -3

• -2

• 2

• 18

Answer explanation

f(-2)=4(-2)+10

f(-2)=2

When x=-2, then y=2, making the coordinate point (-2, 2) a solution to the function.

What is the linear function that represents this table?

• f(x)=2x+3

• f(x)=-2x+3

• f(x)=2x-6

• f(x)=-2x-6

Answer explanation

The slope can be found by placing the pattern of the y's over the pattern of the x's.

In this case -2/1, or -2.

The y-intercept is where x is 0. The y-intercept here is (0, 3), so b=3.

This makes y=-2x+3 the correct function.

Which is the correct graph for f(x)=3x-4?

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Aubrey and Charlie are driving to a city that is 120 miles from their house.They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h. Write a function that models the distance they drive as a function of time.

• 20x+50y=120

• 120y=-20x+50

• y=-50x+120

• y=-50x+100

Answer explanation

The people have already traveled 20 miles of their 120-mile trip. This makes the distance needing to be traveled 100. 100 becomes the y-intercept.

The slope/rate is -50 for the 50 miles per hour speed, meaning they are taking 50 miles off of their trip for each hour.

Aubrey and Charlie are driving to a city that is 120 miles from their house.They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h.

What is a reasonable domain?

Answer explanation

Time is continuous, making any real number a possibility between 0 to the 2 total hours it would take to get there.

Aubrey and Charlie are driving to a city that is 120 miles from their house.They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h.

What is a reasonable range?

Answer explanation

Distance is also continuous, making any real number between the 0 and 100 miles left of the journey to be a part of the y-values in the range.