Question

1. graphing an exponential function (f-if.7e, f-if.8b)

answer the following questions using the function:

\\f(x) = 2^{x-1} + 3\\

a) identify the transformations applied to \\(f(x) = 2^x\\).

b) state the horizontal asymptote.

c) determine the y-intercept.

d) graph the function:

Explanation:

Analyze transformations of the parent function

$$
LATEXBLOCK0
$$

Determine horizontal asymptote and y-intercept

$$
LATEXBLOCK1
$$

Calculate key points for graphing

$$
LATEXBLOCK2
$$

Answer:

Question 7

a) Transformations:
Shifted right by \(1\) unit and shifted up by \(3\) units.

b) Horizontal Asymptote:
\(y = 3\)

c) y-intercept:
\((0, 3.5)\) or \(y = 3.5\)

d) Graph of the function:
The graph has a horizontal asymptote at \(y = 3\), passes through the \(y\)-intercept at \((0, 3.5)\), and contains the points \((1, 4)\), \((2, 5)\), and \((3, 7)\).