Begin by making a table of values for f(x) and its parent function.
See solution.
Practice makes perfect
We will investigate the difference between the y-intercept of an exponential function with both a stretch and a translation and its parent function. Let g(x) be the parent function of f(x).
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Given Function & & Parent Function [0.5em]
f(x)=3(0.7)^x+2 & &g(x)=(0.7)^x
Let's make a table of values for both of them.
x
"3(0.7)^x+2
"f(x)
(0.7)^x
g(x)
-2
3(0.7)^(-2)+2
≈ 8.12
(0.7)^(-2)
≈ 2.04
0
3(0.7)^0+2
5
(0.7)^0
1
2
3(0.7)^2+2
3.47
(0.7)^2
0.49
4
3(0.7)^4+2
≈ 2.72
(0.7)^4
≈ 0.24
Now, we will plot the points on the same coordinate plane and connect them for each function with a smooth curve.
Looking at the graphs, we can immediately determine the y-intercept.
y-intercept of g(x):& 1
y-intercept of f(x):& 5
At first, we can say that the y-intercept of f(x) is 4 more than the y-intercept of its parent function. However, let's consider the given function one last time.
f(x)=3(0.7)^x+ 2
It would be more accurate to say that the y-intercept of f(x) is 2 units more than 3 times the y-intercept of its parent function. This is because the graph of f(x) is a vertical stretch by a factor of 3 followed by a translation 2 units up.
