ACT 1 Alg: Find domain and range - One Minute Per Question

Welcome to your ACT 1 Alg: Find domain and range

$Q_{1}:$ The domain of $f(x)=\frac{\sqrt{(4-x)}}{x-2}$ is

$\left \{ x\mid x\leq 4 \text{ and } x\neq 2 \right \}$

$\left \{ x\mid x\leq 4 \right \}$

$\left \{ x\mid x\neq 2 \right \}$

$\left \{ x\mid x\geq 4 \right \}$

$Q_{2}:$The domain of $f(x)=\frac{3x+6}{x-1}$ is

$\left \{ x\mid x\neq 2 \right \}$

$\left \{ x\mid x\neq 6 \right \}$

$\left \{ x\mid x\neq 1 \right \}$

$\left \{ x\mid x\in \mathbb{R} \right \}$

$Q_{3}:$ The domain of $f(x)=\frac{\sqrt[3]{(4-x)}}{x^{2}-25}$ is

$\left \{ x\mid x\in \mathbb{R} \right \}$

$\left \{ x\mid x\neq 4 \right \}$

$\left \{ x\mid x\neq 5,-5 \right \}$

$\left \{ x\mid x\neq 4,5,-5 \right \}$

$Q_{4}:$ The domain of $f(x)=3x+15$ is

$\left \{ x\mid x\neq -5 \right \}$

$\left \{ x\mid x\in \mathbb{R} \right \}$

$\left \{ x\mid x\leq -5 \right \}$

None

$Q_{5}:$ The range of $f(x)=x^{2}-4x+5$ is

$\left \{ y\mid y\geq 1 \right \}$

$\left \{ y\mid y\leq 1 \right \}$

$\left \{ y\mid y< 1 \right \}$

$\left \{ y\mid y>1 \right \}$

$Q_{6}:$ The range of $f(x)=x^{2}-4x+4$ is

$\left \{ y\mid y< 0 \right \}$

$\left \{ y\mid y\leq 0 \right \}$

$\left \{ y\mid y\geq 0 \right \}$

$\left \{ y\mid y> 0 \right \}$

$Q_{7}:$ If $f(x)=-x$ and $g(x)=x^{2}+6x-8$, then the range of $(f\circ g)(x)$ is

$\left \{ y\mid y\in \mathbb{R} \right \}$

$\phi$

$\left \{ y\mid y>0 \right \}$

$\left \{ y\mid y\leq 17 \right \}$

$Q_{8}:$ If $f(x)=\sqrt[3]{x}$ and $g(x)=-x^{2}-2$, then the domain of $(f\circ g)(x)$ is

$\left \{ x\mid x\leq -2 \right \}$

$\phi$

$\left \{ x\mid x\geq -2 \right \}$

$\left \{ x\mid x\in \mathbb{R} \right \}$

$Q_{9}:$ If $f(x)=\sqrt{x}$ and $g(x)=(x+2)^{2}$, then the range of $(f\circ g)(x)$ is

$\left \{ y\mid y\in \mathbb{R} \right \}$

$\phi$

$\left \{ y\mid y\leq 0 \right \}$

$\left \{ y\mid y\geq 0 \right \}$

$Q_{10}:$ If $f(x)=2x+3$ and $g(x)=x^{2}-1$, then the domain of $(f\circ g)(x)$ is

$\left \{ x\mid x\geq -1 \right \}$

$\phi$

$\left \{ x\mid x\geq 1 \right \}$

$\left \{ x\mid x\in \mathbb{R} \right \}$

$Q_{11}:$ Which of the following expresses the domain of $V(x)=\sqrt{\frac{1}{x-8}}$ ?

$\left \{ x\mid x >8 \right \}$

$\left \{ x\mid x <8 \right \}$

$\left \{ x\mid x \leq 8 \right \}$

$\left \{ x\mid x \geq8 \right \}$

$Q_{12}:$ If $f(x)=2x-1$ and $g(x)=\frac{x-1}{3}$, then the domain of $(f\circ g)(x)$ is

$\left \{ x\mid x\geq 3 \right \}$

$\left \{ x\mid x\geq -1 \right \}$

$\left \{ x\mid x\geq 1 \right \}$

$\left \{ x\mid x\in \mathbb{R} \right \}$

$Q_{13}:$ What is the domain of the function $f(x)=\frac{(x-2)^3}{(x+2)^2}$

All real numbers

$\left \{ x\mid x\neq 2 \right \}$

$\left \{ x\mid x\neq -2 \right \}$

$\left \{ x\mid x<-2 \text{ or } x<2 \right \}$

$Q_{14}:$ The domain of each of the following includes $–5$ EXCEPT

$\frac{1}{x^{2}+25}$

$\sqrt{ \left | x-1\right |} $

$\left | \sqrt{x-1} \right |$

$\frac{1}{5-x}$

$Q_{15}:$ If $f(x)=\frac{x^{2}-1}{3-2x}$ which of the following numbers is NOT in the domain of $f$ ?

$0.66$

$0$

$1$

$1.5$

$Q_{16}:$ If $f(x)=\frac{x^{2}-16}{x^{2}+9}$ which of the following numbers is NOT in the domain of $f$ ?

$-4$

$-3$

$3$

All real numbers are in the domain`

$Q_{17}:$ What is the range of the function $f (x) = (x – 2)^{ 2} + 2$?

All real numbers

All real numbers not equal to 2

All real numbers not equal to –2

All real numbers greater than or equal to 2

$Q_{18}:$ What is the range of the function $f (x) = \sqrt{x^{ 2}-4}$?

All real numbers

All real numbers between –2 and 2, inclusive.

All real numbers greater than or equal to 0

All real numbers greater than or equal to 2 or less than or equal to –2

$Q_{19}:$ If $f(x)=\frac{x^{2}-16}{x^{2}+9}$ which of the following numbers is NOT in the range of $f$ ?

$1$

$0.5$

$0$

$-0.5$

$Q_{20}:$ If $f(x)=\left | -x^{2}-8 \right |$ for all real numbers $x$, then which of the following sets is the range of $f$ ?

$\left \{ y\mid y\geq 8 \right \}$

$\left \{ y\mid y\geq -8 \right \}$

$\left \{ y\mid y\leq 8 \right \}$

$\left \{ y\mid y\leq -8 \right \}$

$Q_{21}:$ If $f(x) = 4x − 5$ for $\left [ 0,10 \right ]$, then which of the following sets represents the range of $f $?

$\left \{ y\mid -5\geq y \geq 35 \right \}$

$\left \{ y\mid -5\leq y \leq 35 \right \}$

$\left \{ y\mid y \leq 35 \right \}$

$\left \{ y\mid y \geq -5 \right \}$

$Q_{22}:$ If $f(x) = x^{2}$ for $0 \leq x \leq 6$, what is the range of $f$ ?

$\left \{ y\mid 0< y <36 \right \}$

$\left \{ y\mid 0\leq y \leq 36 \right \}$

$\left \{ y\mid y \leq 36 \right \}$

$\left \{ y\mid y \geq 0 \right \}$

$Q_{23}:$ If $T(a) =\frac{a^{2}+5}{3}$, then which of the following sets is the range of $T$?

$\left \{ y\mid y \neq 0 \right \}$

$\left \{ y\mid y \geq 0 \right \}$

$\left \{ y\mid y \geq 0.60 \right \}$

$\left \{ y\mid y \geq 1.67 \right \}$

$Q_{24}:$ If $f(x) = 4x+3$ for $-1 \leq x \leq 4$, then which of the following gives the range of $f$ ?

$\left \{ y\mid 1\leq y \leq 19 \right \}$

$\left \{ y\mid -1\leq y \leq 19 \right \}$

$\left \{ y\mid -1\leq y \leq 7 \right \}$

$\left \{ y\mid 1\leq y \leq 7 \right \}$

$Q_{25}:$ If $y = h(x)$ is graphed bellow, which of the following sets could be the range of h(x) ?

$\left \{ y\mid y \leq -3 \text{ or } y \geq -1 \right \}$

$\left \{ y\mid -3\leq y \leq 3 \right \}$

$\left \{ y\mid y \geq -1 \right \}$

$\left \{ y\mid y \geq -3 \right \}$

$Q_{26}:$ If $y = f(x)$ is graphed bellow, which of the following sets could be the range of $f(x)$ ?

$\left \{ y\mid y \leq 2 \right \}$

$\left \{ y\mid y =-2,3 \right \}$

$\left \{ y\mid -2\leq y \leq 3 \right \}$

$\left \{ y\mid 1\leq y \leq 2 \right \}$

$Q_{27}:$ Which of the following expresses the domain of values of $y = k(x)$, if $k(x)=\frac{5}{x+4}$ ?

$\left \{ x\mid x \neq 0 \right \}$

$\left \{ x\mid x \neq 1.25 \right \}$

$\left \{ x\mid x \neq -4.00 \right \}$

$\left \{ x\mid x > 0 \right \}$

$Q_{28}:$ Which of the following expresses the range of values of $y = k(x)$, if $k(x)=\frac{5}{x+4}$ ?

$\left \{ y\mid y \neq 4 \right \}$

$\left \{ y\mid y \neq 1.25 \right \}$

$\left \{ y\mid y \in \mathbb{R} \right \}$

$\left \{ y\mid y \neq 0 \right \}$

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