Answer:
As the function has been shifted up by 2 and is less steep than the function f(x) = 3x-5.
Thus, option C is true. i.e. g(x)=x-3
Step-by-step explanation:
Given the function
[tex]f(x) = 3x-5[/tex]
writing in the slope-intercept form
[tex]y = mx+b[/tex]
where m is the line and b is the y-intercept
To move a function up, we need to add outside the function.
[tex]f(x) + b[/tex] means [tex]f(x)[/tex] moved up 'b' units.
So, by shifting up by 2 means f(x) would become g(x)= 3x-5+2 = 3x-3
But, we have to find the function which is less steep, meaning having a slope less than 3.
so, the best-suited function that has been shifted up by 2 and is less steep than the function f(x) = 3x-5 will be:
A graph is also attached.
- In the graph, the red line represents f(x)=3x-5, and the blue line is representing the function g(x)=x-3 which has been shifted up by 2 and is less steep than the function f(x) = 3x-5.
As the function has been shifted up by 2 and is less steep than the function f(x) = 3x-5.
Thus, option C is true.
