What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(9x)? a) shifts the line 9 units left b) shifts the line 9 units right c) increases the slope of the line by a factor of 9 d) decreases the slope of the line by a factor of 9

option: C is correct.

Step-by-step explanation:

since, we are given a parent function f(x) as: f(x)=x.

We are asked to find what  change will occur in the function when the parent function f(x) is replaced by f(9x).

let g(x) be the function formed by replacing f(x) with f(9x) i.e.

g(x)=f(9x)=9x.

clearly the slope of the function g(x)=f(9x) is 9.  ( since on comparing the equation with the slope intercept form y=mx+c; where m is the slope of the line and c is the y- intercept).

whereas the slope of the function f(x)=x is 1.

Hence there is an increment of slope by a factor of 9.

Hence, option C is correct.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c