*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **10, e−1 , (0, 1), and (−10, e).
Since none of these changes aﬀected the y values, the horizontal asymptote remains y = 0.
Next, we see that the output from f is being multiplied by 90. This results in a vertical
stretch by a factor of 90. We multiply the y -coordinates by 90 to obtain 10, 90e−1 , (0, 90),
and (−10, 90e). We also multiply the y value of the horizontal asymptote y = 0 by 90, and it
remains y = 0. Finally, we add 70 to all of the y -coordinates, which shifts the graph upwards to
obtain 10, 90e−1 + 70 ≈ (10, 103.11), (0, 160), and (−10, 90e + 70) ≈ (−10, 314.64). Adding
70 to the horizontal asymptote shifts it upwards as well to y = 70. We connect these three
points using the same shape in the same direction as in the graph of f and, last but not least,
we restrict the domain to match the applied domain [0, ∞). The result is below.
7 We will discuss this in greater detail in Section 6.5. 334 Exponential and Logarithmic Functions y
180 y
7 160 6 140 5 120 4 100 3 80 2 60 H.A. y = 70 40 (0, 1) 20
−3 −2 −1
12
H....

View
Full
Document