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Precalculus : Graphing Functions

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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:

(x+y)^2 = 1 , where both and are non-negative.

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

Possible Answers:

Curved line passing through the point (0.6, 0.9)

Straight line passing through the point (0.5, 0.5)

Parabola opening up passing through the point (1, 0.5)

Straight line passing through the point (0.5, 1)

Correct answer:

Straight line passing through the point (0.5, 0.5)

Explanation:

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

(x+y)^2 = 1

(x+y) = 1

y = 1 - x

As a simple test, all other values when substituted into the original equation fail. However, (0.5 + 0.5)^2 = 1 works. Therefore (0.5,0.5) is our answer.

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Example Question #1 : Graphing Quadratic Functions

What is the y-intercept of the following equation?

$f(x)=4\sin{3x}+2$

Possible Answers:

(4,0)

(0,2)

(0,3)

(0,4)

(2,0)

Correct answer:

(0,2)

Explanation:

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

$f(0)=4\sin(3*0)+2$

f(0)=4*0+2

f(0)=2

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Example Question #2 : Graphing Functions

Determine the y intercept of f(x) , where $f(x)=\frac{x-4}{x^{2}+x-12}$ .

Possible Answers:

(12,0)

(4,0)

(0,12)

$\bigg(\frac{1}{3},0\bigg)$

$\bigg(0,\frac{1}{3}\bigg)$

Correct answer:

$\bigg(0,\frac{1}{3}\bigg)$

Explanation:

In order to determine the y-intercept of f(x) , set x=0

$f(0)=\frac{0-4}{0^{2}+0-12}$

$f(0)=\frac{-4}{-12}$

$f(0)=\frac{1}{3}$

Solving for y, when x is equal to zero provides you with the y coordinate for the intercept. Thus the y-intercept is $\bigg(0,\frac{1}{3}\bigg)$ .

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Example Question #3 : Graphing Functions

What is the -intercept of the function,

f(x)=(x-2)^2+4 ?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept we need to find the cooresponding value when x = 0 .

Substituting x = 0 into our function we get the following:

f(0)=(0-2)^2+4

f(0)=4+4

f(0)=8

Therefore, our -intercept is .

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Example Question #4 : Graphing Functions

What is the value of the -intercept of f(x)=(2x+4)^2+5 ?

Possible Answers:

The graph does not have a -intercept

Correct answer:

Explanation:

To find the -intercept we need to find the cooresponding value when x=0 . Therefore, we substitute in x=0 and solve:

f(0)=(2(0)+4)^2+5

f(0)=(0+4)^2+5

f(0)=16+5

f(0)=21

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Example Question #1 : Symmetry

If f(x) = f(-x) , what kind of symmetry does the function f(x) have?

Possible Answers:

Symmetry across the line y=x

No Symmetry

Odd Symmetry

Even Symmetry

Correct answer:

Even Symmetry

Explanation:

The definition of even symmetry is if f(x) = f(-x)

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Example Question #2 : Symmetry

If f(-x)=-f(x) , what kind of symmetry does f(x) have?

Possible Answers:

Even symmetry

Symmetry across the line y=x

No symmetry

Odd symmetry

Correct answer:

Odd symmetry

Explanation:

f(-x)=-f(x) is the definition of odd symmetry

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Example Question #1 : Angles

Solve for .

(Figure not drawn to scale).

Possible Answers:

8^o

12^o

10^o

14^o

Correct answer:

14^o

Explanation:

The angles are supplementary, therefore, the sum of the angles must equal 180^o .

$\small (4n+22^o)+(8n-10^o)=180^o$

$\small 4n+22^o+8n-10^o=180^o$

$\small 12n+12^o=180^o$

$\small 12n=168^o$

$\small n=14^o$

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Example Question #1 : Angles

Are $129^{\circ}$ and $51^{\circ}$ supplementary angles?

Possible Answers:

Not enough information

Yes

Correct answer:

Yes

Explanation:

Since supplementary angles must add up to $180^{\circ}$ , the given angles are indeed supplementary.

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Example Question #1 : Angles

Solve for and .

(Figure not drawn to scale).

Possible Answers:

$\small x=15^o;\ y=52.5^o$

$\small x=15^o;\ y=37.5^o$

$\small x=7.5^o;\ y=18.75^o$

$\small x=15^o;\ y=7.5^o$

Correct answer:

$\small x=15^o;\ y=37.5^o$

Explanation:

The angles containing the variable all reside along one line, therefore, their sum must be 180^o .

$\small 5x+4x+3x=180^o$

$\small 12x=180^o$

$\small x=15^o$

Because and are opposite angles, they must be equal.

$\small 2y=5x$

$\small x=15^o$

$\small 2y=5(15^o)=75^o$

$\small y=\frac{75^o}{2}=37.5^o$

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Precalculus : Graphing Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Graphing Functions

Example Question #1 : Graphing Quadratic Functions

Example Question #2 : Graphing Functions

Example Question #3 : Graphing Functions

Example Question #4 : Graphing Functions

Example Question #1 : Symmetry

Example Question #2 : Symmetry

Example Question #1 : Angles

Example Question #1 : Angles

Example Question #1 : Angles

All Precalculus Resources

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