Question

drag and drop the answer that matches each graph. you will either match the graph with an equation or a transformation. every answer choice will not be used
a. graph with point (0,2)
b. graph with point (2,1)
c. graph with point (0,-1)
e. graph with point (0,1)
f. graph with point (0,-3)
g. graph with point (2,-1)
drag & drop the answer
$y = 3^{x+2}$
$y = 3^x + 1$
$y = 3^x$ shifted left 2
$y = 3^{-x}$
$y = 3^{x-2}$
$y = 3^x$ shifted down 4
$y = 3^{x-2} + 1$
$y = 3^x - 2$
$y = 3^x$ reflected over the x and y axis
$y = 3^x$ reflected over the x-axis and shifted left 2
$y = -3^{x - 2}$
$y = 3^x$ with no transformations
$y = 3^x$ reflected over the x-axis
note: use ctrl+d to drag the option via keyboard

Explanation:

Step1: Analyze Graph a

The graph passes through (0,2) and is an increasing exponential curve. The parent function is $y=3^x$, which passes through (0,1). This is shifted up 1, so $y=3^x + 1$.

Step2: Analyze Graph b

The graph passes through (2,1). For $y=3^{x-2}$, when $x=2$, $y=3^{0}=1$, which matches.

Step3: Analyze Graph c

The graph passes through (0,-1) and is a decreasing exponential curve. Reflecting $y=3^x$ over the x-axis gives $y=-3^x$, which passes through (0,-1) and decreases.

Step4: Analyze Graph e

The graph passes through (0,1) and is a decreasing exponential curve. This is $y=3^{-x}$, since $3^{-0}=1$, and it decreases as x increases.

Step5: Analyze Graph f

The graph passes through (0,-3) and is an increasing exponential curve. The parent $y=3^x$ shifted down 4 would be $y=3^x - 4$, but this passes through (0,-3) ($3^0 -4=1-4=-3$), which matches.

Step6: Analyze Graph g

The graph passes through (2,-1). For $y=-3^{x-2}$, when $x=2$, $y=-3^{0}=-1$, which matches the decreasing curve.

Answer:

a. $y = 3^x + 1$
b. $y = 3^{x-2}$
c. $y = 3^x$ Reflected over the x-axis
e. $y = 3^{-x}$
f. $y = 3^x$ Shifted down 4
g. $y = -3^{x-2}$