Question

Find a function that represents a horizontal stretch of the graph of f(x) = |x + 5|

Answer 1

Find a function that represents a horizontal stretch of the graph of f(x) = |x + 5|?

Answer 2

One possible function that represents a horizontal stretch of the graph of f(x) = |x + 5| is:

g(x) = |(x + 5)/k|

where k is a positive constant that determines the degree of stretching. If k is greater than 1, then the graph of g(x) will be narrower than the graph of f(x), and if k is less than 1, then the graph of g(x) will be wider than the graph of f(x).

For example, if we let k = 2, then g(x) = |(x + 5)/2|, and the graph of g(x) will be half as wide as the graph of f(x), as if we compressed it horizontally. Conversely, if we let k = 0.5, then g(x) = |(x + 5)/0.5| = |2(x + 5)|, and the graph of g(x) will be twice as wide as the graph of f(x), as if we stretched it horizontally.

Answer 3

One possible function that represents a horizontal stretch of the graph of f(x) = |x + 5| is:

g(x) = |(x + 5)/a|

where a is a positive constant that determines the degree of stretching. If a is greater than 1, then the graph of g(x) will be narrower than the graph of f(x), and if a is less than 1, then the graph of g(x) will be wider than the graph of f(x).

For example, if we let a = 2, then g(x) = |(x + 5)/2|, and the graph of g(x) will be half as wide as the graph of f(x), as if we compressed it horizontally. Conversely, if we let a = 0.5, then g(x) = |(x + 5)/0.5| = |2(x + 5)|, and the graph of g(x) will be twice as wide as the graph of f(x), as if we stretched it horizontally.