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High School Math : Functions and Graphs

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #3 : Circle Functions

Find the center and radius of the circle defined by the equation:

(x-3)^2+(y+5)^2=36

Possible Answers:

$\left ( 3,-5 \right )\ and\ r=6$

$\left ( -3,-5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=18$

$\left ( 3,5 \right )\ and\ r=6$

$\left ( -3,5 \right )\ and\ r=6$

Correct answer:

$\left ( 3,-5 \right )\ and\ r=6$

Explanation:

The equation of a circle is: $(x-x_{1})^2+(y-y_{1})^2=r^2$ where is the radius and $(x_{1},y_{1})$ is the center.

In this problem, the equation is already in the format required to determine center and radius. To find the -coordinate of the center, we must find the value of that makes (x-3)^2 equal to 0, which is 3. We do the same to find the y-coordinate of the center and find that y=5 . To find the radius we take the square root of the constant on the right side of the equation which is 6.

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Example Question #4 : Circle Functions

Find the center and radius of the circle defined by the equation:

$(x+12)^{2}+(y+10)^2=100$

Possible Answers:

$\left ( 12,-10 \right )\ and\ r=100$

$\left ( -12,-10 \right )\ and\ r=10$

$\left ( 12,-10 \right )\ and\ r=10$

$\left ( 10,-12 \right )\ and\ r=100$

$\left ( -12,10 \right )\ and\ r=25$

Correct answer:

$\left ( -12,-10 \right )\ and\ r=10$

Explanation:

The equation of a circle is: $(x-x_{1})^2+(y-y_{1})^2=r^2$ where is the radius and $(x_{1},y_{1})$ is the center.

In this problem, the equation is already in the format required to determine center and radius. To find the -coordinate of the center, we must find the value of that makes (x+12)^2 equal to , which is . We do the same to find the y-coordinate of the center and find that y=-10 . To find the radius we take the square root of the constant on the right side of the equation which is 10.

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Example Question #31 : Functions And Graphs

It took Jack 25 minutes to travel 14 miles, what was Jack's average speed in mph?

Possible Answers:

$2.4\ mph$

$1.78\ mph$

$33.6\ mph$

$30.21\ mph$

Correct answer:

$33.6\ mph$

Explanation:

$speed=\frac{distance}{time}$

$speed=\frac{14\ miles}{25\ minutes }$

* We have to change the time from minutes to hours, there are 60 minutes in one hour.

$speed= \frac{14\ miles}{25\ minutes} * \frac{60\ minutes}{1\ hour}$

$speed= 33.6\ mph$

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Example Question #1 : Understanding Polynomial Functions

Let $f(x)=3x^{2}-2$ and g(x)= x+2 . Evaluate f(g(3)) .

Possible Answers:

108

Correct answer:

Explanation:

Substitute into g(x) , and then substitute the answer into f(x) .

g(x)= x+2

g(3)=3+2=5

$f(x)= 3x^{2}-2$

$f(5) =3(5)^{2}-2= 75 -2 = 73$

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Example Question #3 : Understanding Polynomial Functions

Solve the following system of equations:

-x-3y= 4

2x+5y=7

Possible Answers:

$\left ( 1,-5 \right )$

$\left ( -4,10 \right )$

$\left ( 41,-15 \right )$

$\left ( 2,4 \right )$

Infinite solutions.

Correct answer:

$\left ( 41,-15 \right )$

Explanation:

We will solve this system of equations by Elimination. Multiply both sides of the first equation by 2, to get:

-2x-6y=8

Then add this new equation, to the second original equation, to get:

-y = 15

y=-15

Plugging this value of back into the first original equation, gives:

-x-3(-15) = 4

-x = 4- 45

x = 41

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Example Question #1 : Polynomial Functions

List the transformations that have been enacted upon the following equation:

$f(x)=4[6(x-3)]^{4}-7$