Functions and Transformations — Quiz

Question 10 • Precalculus

Consider the function f⁡(x)=x5−3⁢x2+5⁢x. Let g⁡(x)=f⁢(−x+4). Which shows the graphs of f of x and g of x ?

Answer

Image with description On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6) and then curves up through (1, 3). Y = g (x) goes through (4.5, negative 3) through (4, 0) to an inflection point around (3.3, 2.4) and then curves up through (3, 3).

Image with description On a coordinate plane, y = f (x) goes through (negative 0.5, negative 3) and (0, 0) to an inflection point around (0.8, 2.6), and then curves up through (1, 3). Y = g (x) goes through (negative 3, negative 3) to an inflection point around (negative 3.2, negative 2.5) and curves up through (negative 4, 0).

Explanation

Since g(x)=f(4−x), the graph of f is reflected horizontally across the line x=2. A point (a, f(a)) on f becomes (4−a, f(a)) on g. For example, (0, 0) becomes (4, 0), and (1, 3) becomes (3, 3), matching choice A. Choice B places these corresponding points at the wrong x-values.

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