Below is a portion of the graph of a function, y=h(x):

If the graph of y=h(x-3) is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is the sum of the coordinates of that point?

Guest Nov 15, 2019

#1**+2 **

Note that the points (-2,3) and (1, 3) are on h(x)

h (x - 3) shifts the graph of h(x) 3 units to the right...so that the point (-2, 3) becomes (1,3)

So...the two graphs will intersect at (1, 3)

The sum of the coordinates = 1 + 3 = 4

CPhill Nov 15, 2019

#2**+1 **

im not the person who asked this question but, why do we add 3 and not subtract if it says -3............. i know based off of f(x)=(x-h) that the function should move h units to the right,,,,but im confused on why we add and not subtract

Nirvana
Nov 15, 2019

#3**+2 **

This is always confusing

f ( x- a) shifts the graph of f(x) "a" units to the right

f( x + a) shifts the graph of f(x) "a" units to the left

Example

f(x) = x^2 has a vertex at (0, 0)

But

f(x) = (x -3)^2 has a vertex at (3, 0) .......3 units to the right of the original vertex

CPhill
Nov 15, 2019

#5**+2 **

-2f(x) vertically stretches the graph by a factor of 2 and "flips" it over the x axis

f( -2x) horizontally compresses the graph by a factor of 2 (makes it narrower) and "flips" it across the y axis

f(-1/2 x) horizontally compresses the graph by a factor of 1/2 (makes it wider) and "flips" it acroos the y axis

See the last two results here for f(x) = (x - 3)^2 : https://www.desmos.com/calculator/ql7h8ppdc5

CPhill Nov 15, 2019