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Multiple Choice
State whether the graph of will be narrower or wider than & if it opens up or down.
A
Narrower; Down
B
Narrower; Up
C
Wider; Down
D
Wider; Up
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Verified step by step guidance
1
Identify the parent function given: \(g(x) = x^2\). This is a standard parabola opening upwards with a vertex at the origin.
Look at the given function: \(f(x) = -\frac{3}{7}x^2\). Notice the coefficient in front of \(x^2\) is \(-\frac{3}{7}\).
Determine the direction the parabola opens by the sign of the coefficient. Since \(-\frac{3}{7}\) is negative, the parabola opens downward.
Compare the absolute value of the coefficient \(\left| -\frac{3}{7} \right| = \frac{3}{7}\) to 1 (the coefficient in \(g(x)\)). Since \(\frac{3}{7} < 1\), the parabola is wider than the parent function.
Combine the observations: the parabola \(f(x)\) opens downward and is wider than \(g(x)\).