Answer to Question #257796 in Math for kleve

Question

Activity 1.1 Answer the guide questions to complete the table of domain and range of the following exponential functions, a.f(x) = 5* Is f(x)=5* defined at any values of x? What is the minimum value of f(x)? Can you determine the the maximum value of f(x)? Domain. Range Set Notation Interval Notation. b. f(x) = (-)" Is f(x) = ()** defined at any values of x? What is the minimum value of f(x)? Can you determine the maximum value of f(x)? Range Set Notation Interval Notation. Domain c. f(x) = (2)³ +3 Which is P(x)? Is a > 0 or a <0? Is P(x) linear? What is the value of h? Set Notation Interval Notation Domain Range d. g(x)=-(4)²-3+1 Which is P(x)? Is a > 0 or a <0? What is the value of h? Is P(x) linear? Set Notation Domain Range Interval Notation

Answer 1

a) $f(x)=5^x$

Is $f(x)=5^x$ defined at any values of $x$ ? Yes.

What is the minimum value of $f(x)$ ? Cannot be defined.

Can you determine the maximum value of $f(x)$ No.

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Domain & Range \\ \hline Set\ notation & \R & \{y\in \R|y>0\} \\ \hdashline Interval\ notation & (-\infin,\infin) & (0,\infin) \end{array}$$

b) $f(x)=(\dfrac{1}{5})^{3x}$

Is $f(x)=(\dfrac{1}{5})^{3x}$ defined at any values of $x$ ? Yes.

What is the minimum value of $f(x)$ ? Cannot be defined.

Can you determine the maximum value of $f(x)$ No.

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Domain & Range \\ \hline Set\ notation & \R & \{y\in \R|y>0\} \\ \hdashline Interval\ notation & (-\infin,\infin) & (0,\infin) \end{array}$$

c) $f(x)=\dfrac{1}{3}(2)^{x}+3$

Which is $P(x)$? $x$ Is $P(x)$ linear? Yes.

Is $a>0$ or $a<0$ ? $a>0$

What is value of $h$ ? $3$

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Domain & Range \\ \hline Set\ notation & \R & \{y\in \R|y>3\} \\ \hdashline Interval\ notation & (-\infin,\infin) & (3,\infin) \end{array}$$

d) $g(x)=-(4)^{2x-3}+1$

Which is $P(x)$? $2x-3$ Is $P(x)$ linear? Yes.

Is $a>0$ or $a<0$ ? $a<0$

What is value of $h$ ? $1$

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Domain & Range \\ \hline Set\ notation & \R & \{y\in \R|y<1\} \\ \hdashline Interval\ notation & (-\infin,\infin) & (-\infin, 1) \end{array}$$

e) $h(x)=2(3)^{3x-1}+2$

Which is $P(x)$? $3x-1$ Is $P(x)$ linear? Yes.

Is $a>0$ or $a<0$ ? $a>0$

What is value of $h$ ? $2$

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Domain & Range \\ \hline Set\ notation & \R & \{y\in \R|y>2\} \\ \hdashline Interval\ notation & (-\infin,\infin) & (2,\infin) \end{array}$$