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Algebra 1 : Algebra 1

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Example Questions

Example Question #2 : How To Graph An Absolute Value Function

Absolute_value

Which of these would most likely be the equation corresponding to the above graph?

Possible Answers:

y = | x + 6 | - 3

y = | x - 6 | - 3

y = | x + 3 | - 6

y = | x - 6 | + 3

y = | x - 3 | - 6

Correct answer:

y = | x + 3 | - 6

Explanation:

This is an absolute value graph. Its equation takes the form y = |x-h|+k , in which h,k represent the number of units that the base graph y = |x| is translated right and up respectively.

Since the graph of y = |x| is translated three units left and six units down, h = -3 and k = -6 .

Plug these values into the general form of the equation:

y = |x-(-3)|+(-6)

Simplify:

y = |x+3|-6

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Example Question #43 : Functions And Lines

$\textup{What is the slope of } y=-4\left | x-2\right | \textup{ when } x=1?$

Possible Answers:

$\textup{It does not exist.}$

Correct answer:

Explanation:

$\textup{When }x=1\textup{ the expression inside the absolute value is negative,} \\\textup{so the function can be written as } y=-4(2-x)=4x-8,\textup{ with a slope of 4.}\\\textup{Plus, the slope changes to -4 when } x>2. \textup{ When } x=2 \textup{ it does not exist.}$

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Example Question #2 : How To Graph An Absolute Value Function

$\textup{Find the lowest attainable value of }y \textup{ in } y=-4+ \left |4x^2-25 \right |.$

Possible Answers:

-2.5

2.5

Correct answer:

Explanation:

$\\ \left | 4x^2-25\right | \textup{cannot get any lower than zero,}\\\textup{so\textit{ y} cannot get any lower than} -4.$

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Example Question #3331 : Algebra 1

$\textup{Which is an \textit{x}-intercept of the function } y=\left | -x^2-8x-16\right |-4.$

Possible Answers:

$\textup{None of the above.}$

Correct answer:

Explanation:

$\\ \textup{The function can be simplified as } \\y=\left | -(x+4)^2\right |-4=\left |(x+4)^2\right |-4=(x+4)^2-4.\\\textup{In order to find the \textit{x}-intercecpt, we solve the equation}\\0=(x+4)^2-4 \textup{ which becomes }\\(x+4)=\pm2\textup{ and has solution } -2 \textup{ and } -6.$

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Example Question #1 : How To Find F(X)

A function is given by $f(x)=3x^{2}+3x-4$ . Find f(2) .

Possible Answers:

Correct answer:

Explanation:

Plugging in 2 wherever is present in the formula yields an answer of 14.

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Example Question #1 : How To Find F(X)

If $f(x) = 0.3x^{2}-9x$ , evaluate f(10) .

Possible Answers:

Correct answer:

Explanation:

To solve this function, we simply need to understand that finding f(10) means that x=10 in this specific case. So, we can just substitute 10 in for .

$0.3(10)^{2}=0.3\cdot 100=30$

is equal to , so our final answer is

30-90 or .

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Example Question #1 : Algebraic Functions

In which of these relations is not a function of ?

Possible Answers:

$y = \left | x-100\right |$

$x^{3}y = -1$

x+y = 1,000,000

$x = y^{2} + 1$

xy = 20

Correct answer:

$x = y^{2} + 1$

Explanation:

In the relation $x = y^{2} + 1$ , there are many values of that can be paired with more than one value of - for example, (2,1),(2,-1) .

To demonstrate that is a function of in the other examples, we solve each for :

x+y = 1,000,000 can be rewritten as y = 1,000,000 -x .

$x^{3}y = -1$ can be rewritten as $y = -\frac{1}{x^{3}}$

xy = 20 can be rewritten as $y = \frac{20}{x}$

$y = \left | x-100\right |$ need not be rewritten.

In each case, we see that for any value of , can be uniquely defined.

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Example Question #3 : How To Find F(X)

f(x)= 2x^2 +x+2

$Evaluate\; f(6)$

Possible Answers:

Correct answer:

Explanation:

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Example Question #1 : How To Find F(X)

What is the next number in the following sequence?

10, 20, 25, 50, 55, 110, 115,...

Possible Answers:

120

230

345

130

155

Correct answer:

230

Explanation:

To form this sequence, alternately multiply by 2 and add 5:

$\begin{matrix} 10 \cdot 2 = 20\\ 20+5 = 25\\ 25 \cdot 2 = 50\\ 50 + 5 = 55\\ 55 \cdot 2 = 110 \\ 110 + 5 = 115 \end{matrix}$

To keep the pattern going, double the seventh term to get the eighth:

$115 \cdot 2 = 230$

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Example Question #2 : How To Find F(X)

Define $f (x) = 3 - \sqrt{x-1}$ and $g\left ( x\right ) = 3 + \sqrt{x-1}$

Evaluate $\left (fg \right ) (13)$

Possible Answers:

$\left (fg \right ) (13)$ is undefined.

Correct answer:

Explanation:

$f (x) = 3 - \sqrt{x-1}$

$f (13) = 3 - \sqrt{13-1} = 3 - \sqrt{12}$

$g(x) = 3 + \sqrt{x-1}$

$g(13) = 3 + \sqrt{13-1} = 3 + \sqrt{12}$

The easiest way to find $\left (fg \right ) (13)$ is to take advantage of the fact that the radical expressons are conjugates, and that their product follows the difference of squares pattern.

$fg (13) = f (13) \cdot g (13) = (3 - \sqrt{12}) (3 + \sqrt{12})= 3^{2} - \left (\sqrt{12} \right )^{2} = 9- 12 = -3$

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2 : How To Graph An Absolute Value Function

Example Question #43 : Functions And Lines

Example Question #2 : How To Graph An Absolute Value Function

Example Question #3331 : Algebra 1

Example Question #1 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #1 : Algebraic Functions

Example Question #3 : How To Find F(X)

Example Question #1 : How To Find F(X)

Example Question #2 : How To Find F(X)

All Algebra 1 Resources

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