Answer :
f(x) = x^2 is the black parabola in both graphs.
g(x) = - 7/2 x^2 tells you the parabola will be:
- flipped upside down because the negative on the 7/2
- skinnier, because of the 7/2.
This will be the second graph.
g(x) = - 7/2 x^2 tells you the parabola will be:
- flipped upside down because the negative on the 7/2
- skinnier, because of the 7/2.
This will be the second graph.
Final answer:
The graph representing the base function f(x) = x^2 is an upward-opening parabola, while the graph for the stretched function g(x) = -\(\frac{7}{2}\)x^2 is a downward-opening, narrower parabola due to the negative coefficient and vertical stretch.
Explanation:
The question asks us to identify which of the graphs represents the base function f(x) = x^2 and the stretched function g(x) = -\(\frac{7}{2}\)x^2. The base function f(x) = x^2 is a parabola opening upwards with its vertex at the origin. The stretched function g(x) is a vertically stretched and reflected version of f(x) since the coefficient -\(\frac{7}{2}\) is negative and greater than 1 in magnitude. This will result in a parabola that opens downwards, and is narrower compared to the base function's graph.
These properties correspond to an even function, which would be symmetric about the y-axis. And since g(x) is just a stretched version of f(x), both graphs will still exhibit symmetry about the y-axis.
A correct graph of these functions would show the parabola for f(x) = x^2 opening upwards, while the graph of g(x) = -\(\frac{7}{2}\)x^2 opens downward and is more "narrow" due to the vertical stretch and reflection implied by the negative coefficient.
