Given the equation y = 3x2 + 4, what is the function of the coefficient of 3 ?
A. It moves the graph of y = 3x2 + 4 three units higher than the graph of y = x2 + 4.
B. It moves the graph of y = 3x2 + 4 three units lower than the graph of y = x2 + 4.
C. It makes the graph of y = 3x2 + 4 wider than the graph of y = x2 + 4.
D. It makes the graph of y = 3x2 + 4 narrower than the graph of y = x2 + 4.
Answer:D
Given the equation y = 3x2 + 4, what is the function of the coefficient of 3 ?
A. It moves the graph of y = 3x2 + 4 three units higher than the graph of y = x2 + 4. B. It moves the graph of y = 3x2 + 4 three units lower than the graph of y = x2 + 4. C. It makes the graph of y = 3x2 + 4 wider than the graph of y = x2 + 4. D. It makes the graph of y = 3x2 + 4 narrower than the graph of y = x2 + 4.
Explanation: D When a function f(x) is transformed into a function of the form f(ax), where a is a constant, if a > 0, the function will be compressed horizontally by a factor of a. Here, y = x2 + 4 can be represented as the parent function, and y = 3x2 + 4 as the transformed function compressed horizontally versus the parent function, and thus narrower, by a factor of 3. This is (D). If you're not sure, try plugging values into each equation to construct a rough graph of each equation and compare them.