Answer:
A. -4
B. 4
C. No values
Step-by-step explanation:
The table represents a linear function [tex]m(x)=ax+b.[/tex] Find a and b:
[tex]2=8a+b\\ \\3=10a+b[/tex]
Subtract these two equations:
[tex]3-2=10a-8a\\ \\2a=1\\ \\a=0.5\\ \\2=8\cdot 0.5+b\\ \\4+b=2\\ \\b=-2[/tex]
Then
[tex]m(x)=0.5x-2[/tex]
Check remaining points:
[tex]m(12)=0.5\cdot 12-2=6-2=4\\ \\m(14)=0.5\cdot 14-2=7-2=5[/tex]
Part A: Find [tex]h(4)-m(16):[/tex]
[tex]h(4)-m(16)=\dfrac{1}{2}(4-2)^2-(0.5\cdot 16-2)=\dfrac{1}{2}\cdot 4-(8-2)=2-6=-4[/tex]
Part B: The y-intercept of the function h(x) is at 2, the y-intercept of the function m(x) is at point -2, then the distance between y-intercepts is
[tex]|2-(-2)|=4[/tex]
Part C: Plot the graphs of the functions h(x) and m(x) (see attached diagram). The graph of the function h(x) is above the graph of the function m(x) for all values of x, so there are no values of x for which m(x) exceed h(x).
