Question

f(x) = -0.3x² + 2. which of the following best describes the transformations f(x) has on the parent function y = x²?

a f(x) is y = x² reflected across the x - axis, vertically compressed by scale factor 2, and translated up 0.3 units.

b f(x) is y = x² vertically compressed by scale factor 0.3 and translated up 2 units.

c none of these

d f(x) is y = x² vertically compressed by scale factor 2 and translated down 0.3 units

e f(x) is y = x² reflected across the x - axis, vertically stretched by scale factor 2, and translated up 0.3 units

f f(x) is y = x² reflected across the x - axis, vertically compressed by scale factor 0.3, and translated up 2 units

Explanation:

Step1: Analyze the coefficient of \(x^2\)

The function is \(f(x)= - 0.3x^{2}+2\). The coefficient of \(x^{2}\) is \(- 0.3\). A negative coefficient means a reflection across the \(x\)-axis. The absolute value of the coefficient, \(| - 0.3|=0.3\), and since \(0 < 0.3<1\), it represents a vertical compression by a scale factor of \(0.3\).

Step2: Analyze the constant term

The constant term is \(+ 2\), which means the graph is translated up 2 units.

Step3: Match with options

Now we check the options. Option F (assuming the last option is F) says \(f(x)\) is \(y = x^{2}\) reflected across the \(x\)-axis, vertically compressed by scale factor \(0.3\), and translated up 2 units, which matches our analysis.

Answer:

F. \(f(x)\) is \(y = x^{2}\) reflected across the \(x\)-axis, vertically compressed by scale factor \(0.3\), and translated up 2 units