Graphing Exponential Functions

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Show your work for each problem.

1.
What is the y-intercept of the graph of $y = 5 \cdot 3^x$ ?
1. a) $(0, 15)$
2. b) $(5, 0)$
3. c) $(0, 5)$
4. d) $(0, 3)$
2.
Which graph falls from left to right?
1. a) $y = 0.5 \cdot 3^x$
2. b) $y = 2 \cdot (1.1)^x$
3. c) $y = 4 \cdot (0.3)^x$
4. d) $y = 4 \cdot 2^x$
3.
What is the horizontal asymptote of $y = 2^x - 7$ ? Enter the number $k$ in $y = k$ .
4.
For $f(x) = 3 \cdot 2^x$ , find $f(-1)$ . Give your answer as a decimal or a fraction.
5.
Make a table of values for $y = 4 \cdot 2^x$ . What is $y$ at $x = 3$ ?
6.
Make a table of values for $y = 6 \cdot (0.5)^x$ . What is $y$ at $x = 3$ ? Give a decimal.
7.
The graph of $y = 2^x$ is shifted 3 units left and 1 unit down. Which equation describes the new graph?
1. a) $y = 2^{x-1} + 3$
2. b) $y = 2^{x+3} + 1$
3. c) $y = 2^{x-3} - 1$
4. d) $y = 2^{x+3} - 1$
8.
What is the range of $y = -4 \cdot 2^x + 1$ ?
1. a) $y > -4$
2. b) $y < 1$
3. c)all real numbers
4. d) $y > 1$
9.
The graph of $y = 3^{x+2} - 5$ crosses the y-axis at $(0, ?)$ . Enter the y-coordinate.
10.
The graph of $y = a \cdot b^x$ passes through $(0, 5)$ and $(2, 45)$ , with $b > 0$ . Find $b$ .
11.
The graph of $y = a \cdot b^x$ passes through $(0, 3)$ and $(1, 6)$ . Find the equation and the value of $y$ at $x = 4$ .
12.
For $y = 2^{x+1} - 4$ , find the asymptote, the y-intercept and the x-intercept. Where does the graph cross the x-axis? Enter the x-coordinate of that point.
13.
Make a table for $y = -3 \cdot 2^x + 2$ and find its asymptote. Give decimals where needed.
14.
Which description matches the graph of $y = -2 \cdot 3^{x-1} + 5$ ?
1. a)Falling, asymptote $y = -5$ , range $y < -5$
2. b)Rising, asymptote $y = 1$ , range $y < 1$
3. c)Rising, asymptote $y = 5$ , range $y > 5$
4. d)Falling, asymptote $y = 5$ , range $y < 5$
15.
The graph of $y = a \cdot b^x$ passes through $(1, 6)$ and $(3, 54)$ , with $b > 0$ . Find $a$ .
16.
The graph of $y = a \cdot b^x$ passes through $(2, 12)$ and $(4, 48)$ , with $b > 0$ . Find the equation and the value of $y$ at $x = 5$ .
17.
A graph of the form $y = a \cdot b^x + 2$ has the asymptote $y = 2$ and passes through $(0, 5)$ and $(1, 11)$ . Find $a$ and $b$ , then the value of $y$ at $x = 2$ .
18.
Find where the graph of $y = 3 \cdot 2^x - 24$ crosses both axes. What is the x-coordinate of the x-intercept?