Lesson 15 - Understanding Functions

What is a function in mathematics?

• A relation where each input has multiple outputs.

• A relation where each input has exactly one output.

• A relation where each output has multiple inputs.

• A relation where inputs and outputs are not related.

Answer explanation

In mathematics, a function is defined as a relation where each input corresponds to exactly one output. This ensures that for every value you input, there is a unique result, making the correct choice the second option.

Which of the following is a linear equation?

Answer explanation

The equation y=2x+5 is linear because it can be expressed in the form y=mx+b, where m and b are constants. The other options involve higher degree terms, making them non-linear.

Which of the following is a non-linear equation?

Answer explanation

The equation x^2 - 4 = 0 is non-linear because it includes a squared term (x^2). The other equations are linear, as they can be expressed in the form y = mx + b or are equivalent to it.

What is the standard form of a linear equation in two variables?

Answer explanation

The standard form of a linear equation in two variables is represented as ax + by = c, where a, b, and c are constants. This format allows for easy identification of the coefficients and the constant term.

• 3

• 4

• -3

• 0

Answer explanation

The equation y = 3x + 4 is in slope-intercept form (y = mx + b), where m is the slope. Here, the slope (m) is 3, which means the correct answer is 3.

Tags

CCSS.8.EE.B.5

• -2

• 5

• 0

• -5

Answer explanation

The y-intercept of a line in the form y = mx + b is the value of b when x = 0. In the equation y = -2x + 5, the y-intercept is 5, which is the correct answer.

Which of the following is a characteristic of a non-linear equation?

• It forms a straight line on a graph.

• It has a constant rate of change.

• It can form a curve on a graph.

• It has no variables.

Answer explanation

A non-linear equation can form a curve on a graph, unlike linear equations that form straight lines. This characteristic distinguishes non-linear equations from others.

Answer explanation

To solve the equation 2x - 4 = 0, add 4 to both sides to get 2x = 4. Then, divide both sides by 2 to find x = 2. Thus, the correct answer is x = 2.

Which of the following is an example of a non-linear function?

Answer explanation

The function y = x^2 + 1 is non-linear because it includes a squared term, which creates a parabolic graph. In contrast, the other options are linear functions, represented by straight lines.

Tags

CCSS.8.F.A.3

Which of the following is a property of a function?

• Each input can have multiple outputs.

• Each output can have multiple inputs.

• Each input has exactly one output.

• Inputs and outputs are not related.

Answer explanation

A function is defined such that each input corresponds to exactly one output. This means that for any given input, there cannot be multiple outputs, making 'Each input has exactly one output' the correct property of a function.