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Algebra II : Functions and Graphs

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Example Question #61 : Functions And Graphs

What is the domain of the function?

$\small f(x)=\sqrt{x}-2$

Possible Answers:

$x\geq2$

$x\geq0$

x>0

x>2

Correct answer:

$x\geq0$

Explanation:

In order for the function to be real, the value inside of the square root must be greater than or equal to zero. The domain refers to the possible values of the independent variable (x-value) that allow this to be true.

$\small \sqrt{x}$

For this term to be real, $\small x$ must be greater than or equal to zero.

$x\geq0$

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Example Question #61 : Introduction To Functions

Give the domain and range for this ellipse.

Dr oval

Possible Answers:

Domain: $-2 \leq x \leq 2$

Range: $-5 \leq y \leq 5$

Domain: x^2 < 25

Range: y^2 < 4

Domain: $x \leq -5$ or $\small x \geq 5$

Range: $\small y \leq -2$ or $\small y \geq 2$

Domain: $-5 \leq x \leq 5$

Range: $-2 \leq y \leq 2$

Domain: all real numbers

Range: $-2 \leq y \leq 2$

Correct answer:

Domain: $-5 \leq x \leq 5$

Range: $-2 \leq y \leq 2$

Explanation:

The domain is the set of all potential x-values. In this case, the graph does not extend to the left of nor to the right of , so the x-values stay between these numbers. We would write this inequality as follows: $-5 \leq x \leq 5$ .

The range is the set of all potential y-values. In this case, the graph does not extend above or below , so the y-values stay between these numbers. We would write this inequality as follows: $-2 \leq y \leq 2$ .

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Example Question #62 : Introduction To Functions

State the domain and range for this parabolic graph:

Dr prac sqrt

Possible Answers:

Domain: $\small x \geq 0$

Range: all real numbers

Domain: $\small x \leq 0$

Range: $\small -5 \leq y \leq 5$

Domain: all real numbers

Range: all real numbers

Domain: $\small x < 0$

Range: $\small -5 < y < 5$

Domain: $\small x > 0$

Range: all real numbers

Correct answer:

Domain: $\small x \geq 0$

Range: all real numbers

Explanation:

The domain is the set of all potential x-values. In this case, the graph starts at x=0 and never extends to the left of this point. This means that $\small x \geq 0$ , inclusive. The range is the set of all potential y-values. In this case, there are no restrictions on the y-axis, so the range is the set of all real numbers.

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Example Question #63 : Introduction To Functions

What is the domain of f(x) ?

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

Possible Answers:

$(-\infty,-3),(-3,\infty)$

$(3,\infty)$

$(-\infty,3),(3,\infty)$

$(-\infty,-3),(3,\infty)$

$(-\infty,3)$

Correct answer:

$(-\infty,3),(3,\infty)$

Explanation:

Based on the denominator, the only value for which f(x) does not exist is x=3 . Therefore, the domain exists for all value except for 3. In interval notation, the domain is

$(-\infty,3),(3,\infty)$

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Example Question #64 : Introduction To Functions

Determine the range of the parabola y=x^2+4 .

Possible Answers:

$y\leq4$

$y\geq-4$

$y\geq4$

$y\leq-4$

All real numbers

Correct answer:

$y\geq4$

Explanation:

The range of a function represents all values of that make the function true. On the other hand, the domain represents all values of that make the function true.

The parabola y=x^2+4 has a range that includes all numbers that are greater than or equal to . This is true because when x=0 , y=4 .

$y=0^{2}+4$

y=4

The range of this parabola is $y\geq4$ .

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Example Question #62 : Functions And Graphs

What is the domain and range of the following graph?

Graph for questions

Possible Answers:

Domain: $x\leq9$

Range: All real numbers

Domain: All real numbers

Range: All real numbers

Domain: All real numbers

Range: $x\leq9$

Domain: All real numbers

Range: $y\leq9$

Domain: $y\leq9$

Range: All real numbers

Correct answer:

Domain: All real numbers

Range: $y\leq9$

Explanation:

Domain looks at x-values and range looks at y-values.

The x-values appear to continue to go on forever, which suggests the answer:

"all real numbers"

The y-values are all number that are equal to nine or less which is

$y\leq9$

So you answer is:

Domain: All real numbers

Range: $y\leq9$

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Example Question #66 : Introduction To Functions

What is the domain of the function $f(x)=\sqrt{x-2}+3$ ?

Possible Answers:

$[3,\infty)$

$[2,\infty)$

$[-2,\infty )$

$[-3,\infty)$

$(-\infty, 2]$

Correct answer:

$[2,\infty)$

Explanation:

The expression under the square root symbol cannot be negative, so to find the domain, set that expression $\geq0$ .

$x-2\geq0$

$x\geq2$

The domain includes all x-values greater than or equal to 2, which can be written as $[2,\infty)$ .

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Example Question #67 : Introduction To Functions

What is the domain of the function $f(x)=\sqrt{7-x}+2$ ?

Possible Answers:

$(-\infty, 2]$

$(-\infty, 7]$

$[7,\infty)$

$[2,\infty)$

$[-7,\infty)$ $[3,\infty)$

Correct answer:

$(-\infty, 7]$

Explanation:

The expression under the square root symbol cannot be negative, so to find the domain, set that expression $\geq0$ .

$7-x\geq0$

$-x\geq-2$

$x\leq7$

The domain includes all x-values less than or equal to 7, which can be written as $(-\infty,7]$ .

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Example Question #62 : Functions And Graphs

What is the range of the function $f(x)=\sqrt{x+4}-6$ ?

Possible Answers:

$(-\infty,-6]$

$[-6,\infty)$

$[4,\infty)$

$[-4,\infty)$

$[-6,\infty)$

Correct answer:

$[-6,\infty)$

Explanation:

The smallest value that the function can have is when the square root part of the function is zero (it cannot be smaller than zero).

0-6=-6

The smallest value is -6, so the range must be $[-6,\infty)$

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Example Question #63 : Functions And Graphs

What is the range of the function $f(x)=-\sqrt{x+7}+3$ ?

Possible Answers:

$[3,\infty)$

$(-\infty,-7]$

$(-\infty,3]$

$(-\infty,-3]$

$[-7,\infty)$

Correct answer:

$(-\infty,3]$

Explanation:

The largest value that the function can have is when the square root part of the function is zero (it cannot be smaller than zero).

-0+3=3

The largest value is 3, so the range must be $(-\infty,3]$

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Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Functions And Graphs

Example Question #61 : Introduction To Functions

Example Question #62 : Introduction To Functions

Example Question #63 : Introduction To Functions

Example Question #64 : Introduction To Functions

Example Question #62 : Functions And Graphs

Example Question #66 : Introduction To Functions

Example Question #67 : Introduction To Functions

Example Question #62 : Functions And Graphs

Example Question #63 : Functions And Graphs

All Algebra II Resources

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