Functions — Quiz 6

Questions in this quiz (10)

1. The given equation defines the function $$g(x) = 3x^2 - 18x + 40$$. For what value of $$x$$ does $$g(x)$$ reach its minimum?

   • -18
   • 18
   • 3
   • -2

2. If $$f(x) = x^2 + 1$$ and $$g(x)$$ is the line in the standard $$xy$$-coordinate plane passing through the points $$(1, f(1))$$ and $$(4, f(4))$$, what is the $$y$$-coordinate of the $$y$$-intercept of $$g(x)$$?

   • -5
   • 2
   • 5
   • -3

3. The function $$f$$ is defined by $$f(x) = 2^x$$. The function $$g$$ is a decreasing linear function. In the $$xy$$-plane, the graphs of $$y = f(x)$$ and $$y = g(x)$$ intersect at two points $$(a, j)$$ and $$(b, k)$$, where $$a$$ < $$b$$. When $$g(x)$$ > $$f(x)$$, which of the following must be true?

   • $$x$$ > $$b$$
   • $$x$$ < $$a$$
   • $$a$$ < $$x$$ < $$b$$
   • $$x$$ < $$a$$ or $$x$$ > $$b$$

4. If $$g(x) = 2x + 1$$ for $$x$$ < $$4$$ and $$g(x) = x + 3$$ for $$x \geq 4$$, what is $$g(g(g(4)))$$?

   • 10
   • 7
   • 13
   • 4

5. If $$f(x)=\frac{4x+5}{6x-7}$$, find $$f^{-1}(x)$$.

   • $$\frac{7x+5}{6x-4}$$
   • $$\frac{7x}{6x-4}$$
   • $$\frac{7x-5}{6x+4}$$
   • $$\frac{5}{6x}$$

6. If $$f(x)=\sqrt[3]{4x+9}$$, what is $$f^{-1}(x)$$?

   • $$\frac{x^3-9}{4}$$
   • $$\sqrt{\frac{x^3+9}{4}}$$
   • $$\frac{x^2-9}{3}$$
   • $$\frac{x^3-4}{9}$$

7. If $$f(x)=\log(5x-7)$$, what is $$f^{-1}(x)$$?

   • $$\frac{10^x-7}{5}$$
   • $$\frac{5^x-7}{10}$$
   • $$\frac{10^x+7}{5}$$
   • $$\frac{5^x+7}{10}$$

8. If $$f(x)=3^{4x+6}$$, about what is $$f^{-1}(150)$$?

   • $$\log(3)$$
   • $$\frac{\log(50)}{\log(3)}$$
   • $$\log(50)$$
   • $$\frac{\frac{\log(150)}{\log(3)}-6}{4}$$

9. Which of these is the intersection point of the asymptotes of the rational function: $$y=\frac{x^2}{x-3}$$

   • $$(-3,2)$$
   • $$(3,6)$$
   • $$(3,3)$$
   • $$(-3,3)$$

10. Which of these is the intersection point of the asymptotes of the function: $$y=\frac{mx+n}{px+q}$$where $$m\neq 0$$ and $$p\neq 0$$?

    • $$(-\frac{q}{p},\frac{m}{p})$$
    • $$(\frac{q}{p},\frac{m}{p})$$
    • $$(-\frac{q}{p},\frac{m}{n})$$
    • $$(-\frac{q}{n},\frac{n}{p})$$