# Common Core: 8th Grade Math : Understand Linear and Nonlinear Functions: CCSS.Math.Content.8.F.A.3

## Example Questions

### Example Question #1 : Graphing Polynomial Functions

Which of the graphs best represents the following function?

None of these

Explanation:

The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve.

### Example Question #1 : How To Graph A Quadratic Function

What is the equation of a parabola with vertex  and -intercept ?

Explanation:

From the vertex, we know that the equation of the parabola will take the form for some  .

To calculate that , we plug in the values from the other point we are given, , and solve for :

Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term:

Distribute the fraction through the parentheses:

Combine like terms:

### Example Question #2 : Introduction To Functions

Which graph depicts a function?

Explanation:

A function may only have one y-value for each x-value.

The vertical line test can be used to identify the function. If at any point on the graph, a straight vertical line intersects the curve at more than one point, the curve is not a function.

### Example Question #21 : Graphing Functions

Which equation best represents the following graph?

None of these

Explanation:

We have the following answer choices.

The first equation is a cubic function, which produces a function similar to the graph. The second equation is quadratic and thus, a parabola. The graph does not look like a prabola, so the 2nd equation will be incorrect. The third equation describes a line, but the graph is not linear; the third equation is incorrect. The fourth equation is incorrect because it is an exponential, and the graph is not an exponential. So that leaves the first equation as the best possible choice.

### Example Question #1 : Graphing Polynomial Functions

None of the above

Explanation:

Starting with

moves the parabola by  units to the right.

Similarly moves the parabola by  units to the left.

Hence the correct answer is option .

### Example Question #3 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #4 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

Next, we can divide each side by

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #5 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

We can add  to both sides:

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #6 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

We can add  to both sides:

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #7 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

Next, we can divide each side by

This equation is in slope-intercept form; thus,  is the correct answer.