1.
Item 1. How many possible solutions does a cubic equation have?
A cubic equation is degree 3, so it can have up to 3 real solutions. Answer: option 4.
2.
Item 4. Write the equation of the graph after it has been compressed vertically by a factor of \(\frac{2}{9}\) from the original graph of \(y=|x+12|\) .
Multiply all y-values by \(\frac{2}{9}\). Answer: D.
3.
Item 5. In the following graph, a function f(x) has been transformed and is represented by g(x). Which transformation best represents g(x)?
g(x) is narrower than f(x), indicating a vertical expansion. Answer: B.
4.
Item 2. The function \(C(f)=\frac{5}{9}(f-32)\) converts a temperature, f degrees Fahrenheit, to C degrees Celsius. Determine \(C(77)\) to the nearest degree.
Substitute: \(C(77)=\frac{5}{9}(77-32)=\frac{5}{9}\times45=25\). Answer: A.
5.
Item 3. Consider the quartic function \(y=\pm(x+p)^4+q\), what happens when \(q\) is positive?
Positive q shifts the graph upward. Answer: A.
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