Answer:
7. f(x) = 4x+1
8. g(x) = 3^x
9. g(x)
Step-by-step explanation:
<h3>7.</h3>
The graph of f(x) is a straight line that crosses the y-axis at y=1, and passes through another grid intersection at (1, 5). This grid intersection is 1 unit right and 4 units up from the y-intercept. This means the slope of the line is ...
slope = rise/run = 4/1 = 4
In slope-intercept form, the function f(x) is ...
f(x) = mx +b . . . . . . where the slope is m and the y-intercept is b
f(x) = 4x +1
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<h3>8.</h3>
The horizontal asymptote and the rapid rate of rise of g(x) tells us this is an exponential function. The generic exponential function is of the form ...
g(x) = a·b^x
The value of 'a' is the y-intercept, which is the same as for f(x). That is, a=1. The value when x=1 is ...
g(1) = a·b^1 = ab
We observe from the graph that g(1) is 3, so ...
g(1) = 3 = ab = 1b ⇒ b = 3
Using the values of 'a' and 'b', we have ...
g(x) = 3^x
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<h3>9.</h3>
We observe that g(x) is already greater than f(x) for x > 2, so g(x) will be greater in the long run.
(In the long run, an exponential function will exceed <em>any</em> polynomial function.)
