Mr. Patel decided to challenge his Algebra I students by asking them to describe the effect 2f would have on the function f(x) = x2. Use your understanding of horizontal and vertical stretches to explain the result. The parabola would stretch both vertically and horizontally by a factor of 2. The parabola would stretch vertically by a factor of 2 and shrink horizontally by a factor of 2. The parabola would shrink vertically by a factor of 2 and stretch horizontally by a factor of 2. The parabola would shrink both vertically and horizontally by a factor of 2.
Mathematics · High School · Thu Feb 04 2021
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The parabola would stretch both vertically and horizontally by a factor of 2.When a constant multiplier is placed directly in front of a function without affecting the x-variable, this causes a vertical stretch if the multiplier is greater than 1 (or a vertical compression if the multiplier is between 0 and 1). There is no horizontal effect because the variable x inside the function doesn't change. Therefore, the graph of f(x) = 2x² would show a parabola that is narrower than the graph of f(x) = x², because the y-values are doubled at every corresponding x-value.