# Precalculus : Graphing Functions

## Example Questions

### Example Question #1 : Graphs

Information about the Hardy Weinberg equation: http://www.nature.com/scitable/definition/hardy-weinberg-equation-299

The Hardy Weinberg equation is a very important concept in population genetics. Suppose we have two "alleles" for a specific trait (like eye color, gender, etc..)  The proportion for which allele is present is given by  and

Then by Hardy-Weinberg:

, where both  and  are non-negative.

Which statement discribes the graph that would appropriately represents the above relation?

Possible Answers:

Parabola opening up passing through the point

Curved line passing through the point

Straight line passing through the point

Straight line passing through the point

Correct answer:

Straight line passing through the point

Explanation:

The equation can be reduced by taking the square root of both sides.

As a simple test, all other values when substituted into the original equation fail.  However,  works. Therefore  is our answer.

### Example Question #1 : Graphing Functions

What is the y-intercept of the following equation?

Possible Answers:

Correct answer:

Explanation:

The y-intercept can by found by solving the equation when x=0. Thus,

### Example Question #2 : Graphing Functions

Determine the y intercept of , where  .

Possible Answers:

Correct answer:

Explanation:

In order to determine the y-intercept of , set

Solving for y, when x is equal to zero provides you with the y coordinate for the intercept. Thus the y-intercept is .

### Example Question #1 : Graphing Functions

What is the -intercept of the function,

?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept we need to find the cooresponding  value when

Substituting  into our function we get the following:

Therefore, our -intercept is .

### Example Question #4 : Graphing Functions

What is the value of the -intercept of ?

Possible Answers:

The graph does not have a -intercept

Correct answer:

Explanation:

To find the -intercept we need to find the cooresponding  value when . Therefore, we substitute in  and solve:

### Example Question #1 : Graphing Functions

If , what kind of symmetry does the function  have?

Possible Answers:

No Symmetry

Odd Symmetry

Symmetry across the line y=x

Even Symmetry

Correct answer:

Even Symmetry

Explanation:

The definition of even symmetry is if

### Example Question #1 : Graphing Functions

If , what kind of symmetry does  have?

Possible Answers:

No symmetry

Even symmetry

Symmetry across the line y=x

Odd symmetry

Correct answer:

Odd symmetry

Explanation:

is the definition of odd symmetry

### Example Question #2 : Angles

Solve for .

(Figure not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

The angles are supplementary, therefore, the sum of the angles must equal .

### Example Question #3 : Angles

Are  and  supplementary angles?

Possible Answers:

Yes

No

Not enough information

Correct answer:

Yes

Explanation:

Since supplementary angles must add up to , the given angles are indeed supplementary.

### Example Question #1 : Angles

Solve for and .

(Figure not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

The angles containing the variable  all reside along one line, therefore, their sum must be .

Because  and  are opposite angles, they must be equal.