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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #54 : Functions

Find the domain and range of the function.

$y=\sqrt{x}$

Possible Answers:

Domain: x>0

Range: All real numbers

Domain: All real numbers

Range: y>0

Domain: $x\ge0$

Range: $y\ge0$

Domain: All real numbers

Range: All real numbers

Correct answer:

Domain: $x\ge0$

Range: $y\ge0$

Explanation:

The domain is the set of x-values for which the function is defined.

The range is the set of y-values for which the function is defined.

Because the values for x are never negative,

and the values for y are never negative,

Domain: $x\ge0$

Range: $y\ge0$

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Example Question #44 : Relations And Functions

What is the domain of $y=\sqrt{x-6}$

Possible Answers:

$[6,\infty)$

$(-6,\infty )$

$[-6,\infty )$

$(-\infty, \infty )$

$(6.\infty )$

Correct answer:

$[6,\infty)$

Explanation:

As long as the number under the square root sign is greater than or equal to , then the corresponding x-value is in the domain. So to figure out our domain, it is easiest to look at the equation and determine what is NOT in the domain. We do this by solving $\sqrt{x-6}=0$ and we get x=6 . We now look at values greater than and less than , and we can see that when x<6 , the number under the square root will be negative. When x>6 , the number will be greater than or equal to . Therefore, our domain is anything greater than or equal to 6, or $[6,\infty )$ .

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Example Question #45 : Relations And Functions

What is the range of y=x^2-4

Possible Answers:

$(-\infty ,-4]$

$(-4,\infty )$

$(4,\infty )$

$[-4,\infty )$

$[4,\infty )$

Correct answer:

$[-4,\infty )$

Explanation:

Because the only term in the equation containing an is squared, we know that its value will range from (when x=0 ) to $\infty$ (as approaches $\infty$ ). When x^2 is large, a constant such as does not matter, but when x^2 is at its smallest, it does. We can see that when x^2=0 , will be at its minimum of . This number gets bracket notation because there is an value such that y=-4 .

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Example Question #1011 : Pre Calculus

What is the domain of the function?

$f(x) = e^{2x^{2}}$

Possible Answers:

$(0, \infty)$

$(-\infty, 1)$

$(-\infty, \infty)$

$(-\infty, 0)$

$(1, \infty)$

Correct answer:

$(-\infty, \infty)$

Explanation:

Any value can be inputed in the exponetial.

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Example Question #1014 : Pre Calculus

Find the domain of the function:

$\frac{1}{\sqrt{x+4}}$

Possible Answers:

$(-\infty,-4]$

$[-4,\infty )$

$(-\infty,\infty )$

$(-\infty,-4)$

$(-4,\infty )$

Correct answer:

$(-4,\infty )$

Explanation:

The square cannot house any negative term or can the denominator be zero. So the lower limit is since cannot be , but any value greater than it is ok. And the upper limit is infinity.

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Example Question #61 : Functions

What is the domain for the function?

$f(x) = \frac{\sqrt{2+3x}}{(x+4)(x-2)}$

Possible Answers:

$(-\infty,-4)\cup(-4,-\frac{2}{3}]\cup[-\frac{2}{3},2 )\cup(2,\infty )$

$(-\infty,\infty)$

$(-4,-\frac{2}{3}]\cup[-\frac{2}{3},2 )$

$[-\frac{2}{3},2 )\cup(2,\infty )$

$(-4,-\frac{2}{3}]\cup[-\frac{2}{3},2 )\cup(2,\infty )$

Correct answer:

$[-\frac{2}{3},2 )\cup(2,\infty )$

Explanation:

The denominator becomes when x = -4 or , so the function does not exist at these points. In numerator, must be at least $-\frac{2}{3}$ or greater to be real. So the function is continuous from $-\frac{2}{3}$ to and to any other value greater than .

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Example Question #61 : Functions

What is the domain of the function below?

$\frac{1}{x^2 + 3x + 2}$

Possible Answers:

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

$(-\infty, -2)\cup(-2,-1)\cup(-1,\infty )$

$(-\infty,\infty )$

$(-\infty,1)\cup(1,2)\cup(2,\infty )$

$(-\infty, -2]\cup[-2,-1]\cup[-1,\infty )$

Correct answer:

$(-\infty, -2)\cup(-2,-1)\cup(-1,\infty )$

Explanation:

The denomiator factors out to:

(x+2)(x+1)

The denominator becomes zero when x = -1,-2 . But the function can exist at any other value.

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Example Question #62 : Functions

What is the domain of the function below?

$\sqrt{3+5x}$

Possible Answers:

$[\frac{3}{5},\infty )$

$(-\infty,3 )$

$[-3,\infty )$

$[-\frac{3}{5},\infty )$

Correct answer:

$[-\frac{3}{5},\infty )$

Explanation:

Cannot have a negative inside the square root. The value of has to be $-\frac{3}{5}$ for the inside of the square root to be at least . This is the lower bound of the domain. Any value of greater than $-\frac{3}{5}$ exists.

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Example Question #1016 : Pre Calculus

f(x) = ln((x+2)(x-3))

Possible Answers:

$(-\infty,\infty )$

$(-\infty,-2 )\cup(-2,3 )\cup(3,\infty )$

(-2,3)

$(3,\infty)$

$(-\infty,-2 )\cup(3,\infty )$

Correct answer:

$(-\infty,-2 )\cup(3,\infty )$

Explanation:

The natural log function does not exist if the inside value is negatuve or zero. The points where the inside becomes negative are x = 3 or . If is greater than , both terms, (x+2) and (x-3) , are positive. If is less than , both terms are negative and multiply to become positive. If the value is between and , only one term will be negative and result in a $ln(-\#)$ , which does not exist.

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Example Question #64 : Functions

What is the domain of the function?

f(x) = ln(3+x)

Possible Answers:

$[-3,\infty)$

$(\frac{1}{3},\infty)$

$[\frac{1}{3},\infty)$

$(-\infty,\infty)$

$(-3,\infty)$

Correct answer:

$(-3,\infty)$

Explanation:

The value inside a natural log function cannot be negative or . At x = -3 , the inside is and any value less than {-3} cannot be included, because result will be a negative number inside the natural log.

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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #54 : Functions

Example Question #44 : Relations And Functions

Example Question #45 : Relations And Functions

Example Question #1011 : Pre Calculus

Example Question #1014 : Pre Calculus

Example Question #61 : Functions

Example Question #61 : Functions

Example Question #62 : Functions

Example Question #1016 : Pre Calculus

Example Question #64 : Functions

All Precalculus Resources

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