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?
+128473 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
+700 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
+128473 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
+700 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)
+128473 -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
