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Sagot :
Answer:
(a) g(x) has a greater slope
(b) g(x) has a greater y intercept
Step-by-step explanation:
Given
[tex]x \to -1,0,1[/tex]
[tex]f(x) \to -5,-1,3[/tex]
[tex]g(x) = 4x + 3[/tex]
Solving (a): Compare the slopes
Slope (m) is calculated as:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, for f(x), we have:
[tex]m =\frac{-1- 0}{-5- -1}[/tex]
[tex]m =\frac{-1}{-4}[/tex]
[tex]m =\frac{1}{4}[/tex]
For g(x), we have:
Assume [tex]g(x) = mx + c[/tex] then the slope is m
Compare the above to [tex]g(x) = 4x + 3[/tex]
Then the slope of g(x) is 4
g(x) has a greater slope
Solving (b): Function with greater y intercept
Here we set [tex]x= 0[/tex]
From the table of f(x)
[tex]f(x) = -1[/tex] when [tex]x = 0[/tex]
From [tex]g(x) = 4x + 3[/tex]
[tex]g(0) = 4 * 0 + 3[/tex]
[tex]g(0) = 3[/tex]
Hence:
g(x) has a greater y intercept
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