SOLUTION: Suppose that the function y = f(x) is increasing on the interval (4, 7). Over what interval is the graph of y = f(x + 8) increasing?

Question 1126553: Suppose that the function y = f(x) is increasing on the interval (4, 7). Over what interval is the graph of
y = f(x + 8) increasing?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
y = f(x+8) is shifted to the left 8 units.

therefore, if f(x) is increasing in the interval of (4,7), then y = f(x + 8) should be increasing in the interval of (-4,-1).

you should be able to take any function and show that this is true.

for example:

let y = f(x) = x^2 - 10

when x = 4, y = 6
when x = 7, y = 39

let y = f(x+8) = (x+8)^2 - 10

when x = -4, y = 6
when x = -1, y = 39

note that -4 + 8 = 4 and -1 + 8 = 7.

so f(4) = 6 and f(-4+8) = f(4).

RELATED QUESTIONS
Suppose that a function y=f(x) is increasing on the interval (-5,2) a.)Over what... (answered by josgarithmetic)

suppose the function y=f(x) is decreasing on the interval (-2,7). Over what interval is... (answered by math_tutor2020)

Suppose that the function y=f(x) is decreasing on the interval (-2,7). Over what interval (answered by ikleyn,MathLover1)

Over what interval of the domains is this function increasing: f(x) = x^2 +... (answered by stanbon)

Graph: f(x)= -|x-1|+4 and determine the interval over which f(x) is an increasing... (answered by jim_thompson5910)

Over what interval is the graph of y = −(x − 2) 2... (answered by josgarithmetic)

y=f(x) is decreasing on the interval (-2,7). what interval is the graph of y=f(x+2)... (answered by MathLover1,ikleyn)

f(x) = x^3 − 2x^2 − 4x + 8 / x − 2 Find any hole(s) in the graph of f. (answered by greenestamps)

On what interval is the function f(x)=x^2-2x-9... (answered by nerdybill)