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

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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?

Nov 15, 2019

#1
+109334
+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

Nov 15, 2019
edited by CPhill  Nov 15, 2019
#2
+683
+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
+109334
+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
#4
+683
0

ohhhhhh i see!

kind of like stretches and compressions!

1/2f(X) vertically compresses the graph
but

f(2x) horizontally compresses the graph as well

and 2f(X) vertically stretches
as f(1/2x) horizontally stretches

but....
what would happen with -2f(x)
and f(-2x) and f(-1/2x)

Nirvana  Nov 15, 2019
#5
+109334
+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

Nov 15, 2019
#6
+683
+1

awesomey sauce! thanks again :D

Nirvana  Nov 15, 2019