The true statement about f(x) and g(x) is (a) the graph of f(x) is less steep than the graph of g(x).
The equations are given as:
![f(x) = -\frac 34x -1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-%5Cfrac%2034x%20-1)
![g(x) = -4f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-4f%28x%29)
Substitute
in ![g(x) = -4f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-4f%28x%29)
![g(x) = -4(-\frac 34x -1)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-4%28-%5Cfrac%2034x%20-1%29)
Expand
![g(x) = 3x + 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20%2B%204)
So, the equations of f(x) and g(x) are:
![f(x) = -\frac 34x -1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-%5Cfrac%2034x%20-1)
![g(x) = 3x + 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20%2B%204)
A linear equation y = mx + b has a slope of m and a y-intercept of b.
So, the slopes of g(x) and f(x) are 3 and -3/4.
So, the y-intercept of g(x) and f(x) are 4 and -1
This means that
- The graph of f(x) is less steep; option (a) is true
- The y-intercept of f(x) is 5 less the y-intercept of g(x); option (b) is false
Both graphs are not the same, and they have different x-intercepts.
Hence, the true statement is (a)
Read more about linear functions at:
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