Unformatted text preview: 4 5 6 7 8 9 10 x horizontal scaling by a factor of 2 1 2 3 4 5 −− − − − − − − − −→
y = f (x) multiply each x-coordinate by 2 y = g (x) = f 6 7 8 9 10 x 1
2 We have the following theorem.
Theorem 1.6. Horizontal Scalings. Suppose f is a function and b > 0. To graph y = f (bx),
divide all of the x-coordinates of the points on the graph of f by b. We say the graph of f has
been horizontally scaled by a factor of 1 .
• If 0 < b < 1, we say the graph of f has undergone a horizontal stretch (expansion, dilation)
by a factor of 1 .
• If b > 1, we say the graph of f has undergone a horizontal shrink (compression, contraction)
by a factor of b.
Theorem 1.6 tells us that if we multiply the input to a function by b, the resulting graph is scaled
horizontally by a factor of 1 since the x-values are divided by b to produce corresponding points
on the graph of f (bx). The next example explores how vertical and horizontal scalings sometimes
interact with each other and with the...
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