# Precalculus : Graphing Functions

## Example Questions

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### Example Question #1 : Graphing Functions

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?

Straight line passing through the point

Straight line passing through the point

Parabola opening up passing through the point

Curved line passing through the point

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 #2 : Graphing Functions

What is the y-intercept of the following equation?

Explanation:

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

### Example Question #3 : Graphing Functions

Determine the y intercept of , where  .

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,

?

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 #1 : Graphing Functions

What is the value of the -intercept of ?

The graph does not have a -intercept

Explanation:

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

### Example Question #1 : Symmetry

If , what kind of symmetry does the function  have?

Even Symmetry

Symmetry across the line y=x

Odd Symmetry

No Symmetry

Even Symmetry

Explanation:

The definition of even symmetry is if

### Example Question #1 : Symmetry

If , what kind of symmetry does  have?

Symmetry across the line y=x

Even symmetry

Odd symmetry

No symmetry

Odd symmetry

Explanation:

is the definition of odd symmetry

### Example Question #2 : Graphing Functions

Solve for .

(Figure not drawn to scale).

Explanation:

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

### Example Question #1 : Angles

Are  and  supplementary angles?

Yes

No

Not enough information

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).