# SAT II Math I : Solving Functions

## Example Questions

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### Example Question #1 : Solving Linear Functions

Solve for  in terms of .

Explanation:

First, subtract 7 to both sides.

Factor the y on the left hand side.

Divide both sides by 3 – x.

Take an extra step by factoring the minus sign on the denominator.

Cancel the minus signs.

### Example Question #2 : Solving Linear Functions

Find the equation for the line goes through the two points below.

Explanation:

Let .

First, calculate the slope between the two points.

Next, use the slope-intercept form to calculate the intercept. We are able to plug in our value for the slope, as well the the values for .

Using slope-intercept form, where we know and , we can see that the equation for this line is .

### Example Question #3 : Solving Linear Functions

Find the equation of the line passing through the points and .

Explanation:

To calculate a line passing through two points, we first need to calculate the slope, .

Now that we have the slope, we can plug it into our equation for a line in slope intercept form.

To solve for , we can plug in one of the points we were given. For the sake of this example, let's use , but realize either point will give use the same answer.

Now that we have solved for b, we can plug that into our slope intercept form and produce and the answer

### Example Question #4 : Solving Linear Functions

Find the point at which these two lines intersect:

Explanation:

We are looking for a point, , where these two lines intersect. While there are many ways to solve for and given two equations, the simplest way I see is to use the elimination method since by adding the two equations together, we can eliminate the variable.

Dividing both sides by 7, we isolate y.

Now, we can plug y back into either equation and solve for x.

Next, we can solve for x.

Therefore, the point where these two lines intersect is .

### Example Question #5 : Solving Linear Functions

Solve for  when .

Explanation:

The first thing is to plug in the given value so you equation is

.

Then you must subtract  from both sides in order to get  by itself.

You now have

and you must multiply by  for each side and you get .

### Example Question #1 : Solving Linear Functions

Solve:

Explanation:

Add  on both sides.

Subtract 2 from both sides.

Divide by 10 on both sides.

Reduce the fractions.

### Example Question #1 : Solving Linear Functions

Solve:

Explanation:

Distribute the right side.

Rewrite the equation.

Subtract  on both sides.

Add 4 on both sides.

Divide by three on both sides.

### Example Question #1 : Solving Exponential Functions

Solve the following function:

and

and

Explanation:

You must get  by itself so you must add  to both side which results in

.

You must get the square root of both side to undue the exponent.

This leaves you with .

But since you square the  in the equation, the original value you plug can also be its negative value since squaring it will make it positive anyway.

This means your answer can be  or .

### Example Question #1 : Solving And Graphing Exponential Equations

What is the horizontal asymptote of the graph of the equation  ?

Explanation:

The asymptote of this equation can be found by observing that  regardless of . We are thus solving for the value of as approaches zero.

So the value that  cannot exceed is , and the line  is the asymptote.

### Example Question #2 : Solving And Graphing Exponential Equations

What is/are the asymptote(s) of the graph of the function

?