Question

What is the range of f(x) = -3^x + 4?
A. the set of real numbers less than 4

B. the set of real numbers greater than 4

C. the set of real numbers less than 0

D. the set of real numbers greater than 0

Answer 1

what's the graph of \(\bf y= -3^x \quad ?\)

Answer 2

range will be "the set of real numbers less than 4"
\[y \in \mathbb{R} : y < 4\]

Answer 3

\(\bf \textit{parent function}\quad -3^x\\ \quad \\
\begin{array}{rrllll}
&\textit{flips it upside down}\\
&\downarrow \\
y=&{\color{red}{ -}}3^x&{\color{red}{ +4}}\\
&&\uparrow \\
&&\textit{vertical shift of 4 units}
\end{array}\)

Answer 4

ahemm \(\bf \textit{parent function}\quad -3^x\\ \quad \\
\begin{array}{rrllll}
&\textit{flips it upside down}\\
&\downarrow\quad \\
y=&{\color{red}{ -}}3^x&{\color{red}{ +4}}\\
&&\uparrow \\
&&\textit{vertical shift of 4 units}
\end{array}\) better... there

Answer 5

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIzXngiLCJjb2xvciI6IiNFODE5MTkifSx7InR5cGUiOjEwMDB9XQ-- <--- add the " - " in front of it, press Tab key
then add the " +4 " , press Tab key again

notice the "transformations"

Answer 6

and thus the range

Answer 7

You dont need to go into that detail. If you want to know Domain & Range of a function assume some values of x like {1 , 2 , 3 ....} put them in the equation & by getting answers you will have an idea of the range & domain.