Functions

Which of the following represents a function?

• A set of ordered pairs where each input has multiple outputs

• A set of ordered pairs where each input has exactly one output

• A set of ordered pairs where each output has exactly one input

• A set of ordered pairs where inputs and outputs are the same

Answer explanation

A function is defined as a relation where each input corresponds to exactly one output. Therefore, the correct choice is 'A set of ordered pairs where each input has exactly one output', as it meets this criterion.

Tags

CCSS.8.F.A.1

• Both have the same rate of change

• Cannot be determined

Answer explanation

Both functions have a constant rate of change. For f(x) = 2x + 3, the rate of change is 2. For g(x), the change in g(x) from the table shows a consistent increase of 3 for each increase of 1 in x, also giving a rate of change of 3. Thus, they are the same.

Tags

CCSS.8.F.A.2

Which of the following equations represents a linear function?

Answer explanation

The equation y = 4x - 7 is a linear function because it can be expressed in the form y = mx + b, where m and b are constants. The other equations involve non-linear terms such as x^2, 1/x, and √x.

Tags

CCSS.8.F.A.3

Answer explanation

The total cost C for driving m miles includes a flat fee of 20 and a variable cost of 0.50 per mile. Thus, the function is C(m) = 20 + 0.50m, which matches the correct choice.

Tags

CCSS.8.F.B.4

Which graph best describes a function that is increasing and then decreasing?

• A straight line with a positive slope

• A parabola opening upwards

• A parabola opening downwards

• A horizontal line

Answer explanation

A parabola opening downwards first increases to a maximum point and then decreases, which matches the description of a function that is increasing and then decreasing. The other options do not exhibit this behavior.

Tags

CCSS.8.F.B.5

• 10

• 12

• 14

• 16

Answer explanation

To find the output of f(4), substitute 4 into the function: f(4) = 3(4) + 2 = 12 + 2 = 14. Therefore, the correct answer is 14.

Tags

CCSS.8.F.A.1

• Both are linear

• Neither is linear

Answer explanation

The function g(x) = 2x + 3 is linear because it can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. In contrast, f(x) = x^2 is a quadratic function, not linear.

Tags

CCSS.8.F.A.2

Which of the following is not a linear function?

Answer explanation

The function y = x^2 + 4 is not linear because it contains the term x^2, which makes it a quadratic function. The other options are linear functions, represented by the form y = mx + b.

Tags

CCSS.8.F.A.3

Answer explanation

The total cost C for m miles is 3 for the first mile and 2 for each additional mile. For m > 1, the cost is C(m) = 3 + 2(m-1), which accounts for the first mile and the additional miles.

Tags

CCSS.8.F.B.4

Which graph represents a function that is decreasing throughout?

• A straight line with a negative slope

• A straight line with a positive slope

• A horizontal line

• A parabola opening upwards

Answer explanation

A straight line with a negative slope consistently decreases as you move from left to right. In contrast, a positive slope increases, a horizontal line remains constant, and a parabola opening upwards eventually increases.

Tags

CCSS.8.F.B.5