Question

Graph each function using a table of values, then identify its key characteristics.

Answer 1

$y=3^x-4$

we make the table using 3 any numbers for x and replacing on the function

x=-1

$\begin{gathered} y=3^{-1}-4 \\ y=-\frac{11}{3} \end{gathered}$

x=0

$\begin{gathered} y=3^0-4 \\ y=-3 \end{gathered}$

x=1

$\begin{gathered} y=3^1-4 \\ y=-1 \end{gathered}$

Table

place the points and joint it

the function is growth since it can be seen in the graph

Domain

We can see on graph the line can be any value of x because horizontally it has no beginning or end

$(-\infty,\infty)$

Range

We can see the smallest value that the graph could take is -4 and the May is not defined so it is infinite

$(-4,\infty)$

Y intercept

point where x = 0 and the line touches the y axis

the point is

$(0,-3)$

Asymptote

horizontal or vertical line that the nape line will touch

our asymptote lies on the value of y = -4, why the line never touches this value

$y=-4$