Mini Exam 2
Timed practice exam
Loading quiz...
Frequently Asked Questions
Quick answers based on this quiz content.
The table gives values for a function $$f$$ at selected values of $$x$$. Which of the following statements is true?⌄
Compute first differences: $$1-5=-4$$, $$-1-1=-2$$, $$-1-(-1)=0$$, $$1-(-1)=2$$ Not constant. Compute second differences: $$-2-(-4)=2$$, $$0-(-2)=2$$, $$2-0=2$$ Constant second differences indicate quadratic. Final answer: $$\text{f is quadratic because the second differences are constant}$$
The binomial theorem can be used to expand $$q(x)=(2x-1)^6$$. What is the coefficient of the $$x^4$$ term?⌄
General term: $$\binom{6}{k}(2x)^{6-k}(-1)^k$$ For $$x^4$$: $$6-k=4 \Rightarrow k=2$$ Coefficient: $$\binom{6}{2}(2)^4(-1)^2$$ $$=15\cdot16\cdot1=240$$ Final answer: $$240$$
The table gives polar coordinates $$(r, θ)$$ for four points. Which point lies in Quadrant III?⌄
Quadrant III requires angle between $$\pi$$ and $$\frac{3\pi}{2}$$. Check values. $$\frac{7\pi}{6}$$ lies in Quadrant III. That corresponds to point C. Final answer: $$C$$
In the $$xy$$-plane, two different angles α and β are in standard position and share a terminal ray. Which values of $$α$$ and $$β$$ satisfy this?⌄
Angles sharing terminal side differ by $$2\pi$$ multiples. Only pair that differs by $$2\pi$$ is $$\frac{3\pi}{4}$$ and $$\frac{11\pi}{4}$$. Final answer: $$\text{those angles}$$
In the $$xy$$-plane, the function k is given by $$k(x)=2^{x-3}$$. Which expression represents $$k(x)$$ as a vertical dilation of $$f(x)=2^x$$?⌄
Rewrite: $$2^{x-3}=2^x\cdot2^{-3}=\frac{1}{8}\cdot2^x$$ Final answer: $$\frac{1}{8}2^x$$
The function $$f$$ is given by $$f(x)=3\sin(\pi x)-2$$. The graph of $$f$$ is translated horizontally $$\frac{1}{2}$$ unit to the left to form $$g$$. Which of the following is an expression for $$g(x)$$?⌄
A horizontal shift to the left by $$\frac{1}{2}$$ means replace $$x$$ with $$x+\frac{1}{2}$$. $$g(x)=f\left(x+\frac{1}{2}\right)$$ Substitute into $$f$$. $$g(x)=3\sin\left(\pi\left(x+\frac{1}{2}\right)\right)-2$$ Final answer: $$\text{A}$$
The function $$T$$ models temperature as a function of time $$t$$, and the function $$E$$ models energy usage as a function of temperature. Let $$M(t)=E(T(t))$$. Which of the following best describes $$M$$?⌄
$$T(t)$$ gives temperature from time. $$E(T(t))$$ then gives energy usage from that temperature. So, the input is time. So the output is energy usage. Final answer: $$\text{A}$$
In the $$xy$$-plane, the graph of which of the following functions has a vertical asymptote at $$x=\frac{5\pi}{6}$$?⌄
The graph of $$\tan(u)$$ has vertical asymptotes when $$u=\frac{\pi}{2}+k\pi$$ Test the corrected option $$f(x)=\tan\left(x-\frac{\pi}{3}\right)$$ Set the inside equal to $$\frac{\pi}{2}$$. $$x-\frac{\pi}{3}=\frac{\pi}{2}$$ $$x=\frac{\pi}{2}+\frac{\pi}{3}$$ $$x=\frac{5\pi}{6}$$ So, this function has a vertical asymptote at $$x=\frac{5\pi}{6}$$. Final answer: $$\text{B}$$