Linear Functions

Which has a positive slope?

• Only Function 1

• Only Function 3

• Both functions 1 & 3

• Both functions 2 & 3

Which function has a greater y-intercept, and why?

• Function 2 has a greater y-intercept because 5 > 3.

• Function 1 has a greater y-intercept because 5 > 3.

• Function 2 has a greater y-intercept because -1/2 > -3.

• Function 1 has a greater y-intercept because -1/2 > -3

Which statement is true about the rate of change of the two functions?

• Both functions have negative rates of change.

• Both functions have positive rates of change.

• Function 1 has a negative rate of change, while that of Function 2 is positive.

• Function 1 has a positive rate of change, while that of Function 2 is negative.

A function is a rule that assigns to each input exactly one output. In a graph, the input is the x-value, and the output is the y-value.

Which graph(s) do not represent a function?

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Consider the relation shown in the figure. Which ordered pairs show that the relation is not a function?

• (0,-2) and (0,1)

• (0,1) and (2,1)

• (1, 2) and (3,4)

• None, because this mapping is a function

Which statement describes the definition of a function?

• For every input, there is exactly one output.

• For every input, there are no more than two outputs.

• For every output, there is exactly one input.

• For every output, there are no more than two inputs.

Which function is not linear?

Peter ran to get to school from his house. He stopped to pick up his friend Janet from her house when he realized that forgot his math books. He then ran back to his house to get the books.

Which of these graphs best models Peter's the distance from home?

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The graph shows a jogger’s progress during a workout. The jogger runs a total distance of 3 miles, and the complete workout lasts 25 minutes. Which statement is true?

• The jogger moves at a constant rate of 1 mile every 9 minutes during the first 9 minutes of the workout.

• The jogger moves at a faster rate during the first 5 minutes of the workout than at any other time.

• The jogger moves for only 19 minutes of the workout because the graph only shows a change in distance from minutes 0−7, 9−12, 14−17, and 19−25.

• The jogger moves for only 19 minutes of the workout because the graph only shows a change in distance from minutes 7−9, 12−14, and 17−19.

Which statement is true?

• The graph is decreasing and linear when x is less than −1.

• The graph is decreasing and linear when x is between −1 and 1.

• The graph is decreasing and linear when x is more than 2.

• The graph is decreasing and nonlinear when x is more than 2.