数学代写|预备微积分代考

Problem 1.

1. A bank loaned out \$100,000, part of it at the flat rate of $10\%$ per year and the rest at the flat rate $6\%$ per year. If, after one year, the total interest received on both loans was \$7,600, how much was loaned at $10\%$ ? (Simple interest is paid once, at the end of the year.)
   
   
   
   1. 20,000
      
   2. 30,000
      
   3. 40,000
      
   4. 50,000
      
   5. 60,000
      
   
   

Problem 2.

2. Find the domain of the function $f(x)=\frac{1}{\sqrt{20-2 x}}-\frac{1}{\sqrt{x-5}}$.
   
   
   
   1. $[5,10)$
      
   2. $(5,10)$
      
   3. $[5,20)$
      
   4. $(5,22)$
      
   5. $(-\infty, \infty)$
      
   
   

Problem 3.

3. Which of the following lines is perpendicular to the line given by $2 x+3 y=5$ ?
   
   
   
   1. $y=-\frac{2}{3} x-1$
      
   2. $y=\frac{2}{3} x-2$
      
   3. $y=-\frac{3}{2} x-3$
      
   4. $y=\frac{3}{2} x-4$
      
   5. $x=\frac{5}{2}$
      
   
   

Problem 4.

4. Find the average rate of change for the function $f(x)=|x-1|$ between $x=-1$ and $x=1$.
   
   
   
   1. 1
      
   2. $\frac{1}{2}$
      
   3. 0
      
   4. $-\frac{1}{2}$
      
   5. -1
      
   
   

Problem 5.

5. Consider the piecewise defined function
   $$
   f(x)=\left{\begin{array}{cl}
   -\frac{1}{x} & \text { if } x<0 \
   \frac{1}{x+1} & \text { if } x \geq 0
   \end{array}\right.
   $$
   Evaluate $f(0)+f(1)$.
   
   
   
   1. undefined
      
   2. 0
      
   3. $\frac{1}{2}$
      
   4. 1
      
   5. $\frac{3}{2}$
      
   
   

Problem 6.

6. If you translate the graph of $y=f(x)$ down 3 units and then apply a vertical compression by a factor of $\frac{2}{3}$, you get the graph of
   
   
   
   1. $y=\frac{3}{2} f(x)-3$
      
   2. $y=\frac{2}{3} f(x)+3$
      
   3. $y=\frac{2}{3} f(x)+2$
      
   4. $y=\frac{2}{3} f(x)-3$
      
   5. $y=\frac{2}{3} f(x)-2$
      
   
   

Problem 7. Match the function to the graph shown below:
(a) $f(x)=(x-2)^2+4$
(b) $f(x)=-(x-2)^2+4$
(c) $f(x)=(x+2)^2+4$
(d) $f(x)=-(x+2)^2+4$
(e) $f(x)=-(x-2)^2-4$

Problem 8. The function $f(x)=x /\left(x^2-1\right)$ is
(a) even
(b) odd
(c) not defined at $x=0$
(d) neither even, nor odd
(e) not a function (fails the vertical line test)

Problem 9. Find the inverse of $f(x)=2 x^3+1$.
(a) $\left(\frac{x-1}{2}\right)^3$
(b) $\frac{\sqrt[3]{x}-1}{2}$
(c) $\sqrt[3]{\frac{x+1}{2}}$
(d) $\sqrt[3]{\frac{x-1}{2}}$
(e) $\frac{\sqrt[3]{x-1}}{2}$

Problem 10. Solve the inequality $x^2-2 x+1>4$.
(a) $x<-1$ (b) $x>2$
(c) $-2<x<2$
(d) $-1<x<3$
(e) $x<-1$ or $3<x$

Problem 11. Find the composite function $f \circ g(x)=f(g(x))$, given $f(x)=\frac{1}{x+1}$ and $g(x)=\frac{1}{3 x-1}$.
(a) $\frac{3 x+1}{3 x+2}$
(b) $\frac{3 x+1}{3 x-2}$
(c) $\frac{3 x-1}{3 x}$
(d) $\frac{x+1}{2-x}$
(e) $\frac{1}{3 x}$

Problem 12. Consider the function $f(x)=x^2$ on the interval $[0, \infty)$. What is $f^{-1}(2)$ ?
(a) $-\sqrt{2}$
(b) 0
(c) $\sqrt{2}$
(d) $-\sqrt{2}$ or $\sqrt{2}$
(e) Not defined, $f$ is not one to one.