Precalculus : Graphing Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Pre Calculus

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:

Straight line passing through the point 

Straight line passing through the point 

Curved line passing through the point 

Parabola opening up 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 Quadratic 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 Quadratic 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 #3 : Graphing Quadratic 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 Quadratic 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 : Symmetry

If , what kind of symmetry does the function  have?

Possible Answers:

No Symmetry

Symmetry across the line y=x

Even Symmetry

Odd Symmetry

Correct answer:

Even Symmetry

Explanation:

The definition of even symmetry is if 

Example Question #2 : Symmetry

If , what kind of symmetry does  have?

Possible Answers:

Odd symmetry

No symmetry

Even symmetry 

Symmetry across the line y=x

Correct answer:

Odd symmetry

Explanation:

 is the definition of odd symmetry

Example Question #1 : Linear Functions

Solve for .

Question_2

(Figure not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

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

Example Question #2 : Linear Functions

Are  and  supplementary angles?

Possible Answers:

Not enough information

No

Yes

Correct answer:

Yes

Explanation:

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

Example Question #1 : Finding Angles

Solve for and .

Question_3

(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.

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