Exam 1

1. Show through checking (do not solve) that x = 3 is not a solution to the equation

$5x^2–2x^3+7x=12–x$

2. True or False

$25x^3{(2x^4–5x)}^4–100x{(2x^3–5)}^3$

simplifies to 

3.  Given the graph determine the slope

$$\begin{gathered} a. \frac{–2}{3} \\ b. \frac{–3}{2} \\ c. \frac{3}{2} \\ d. None of the above. \end{gathered}$$

4.   Find the equation of the line that has the same slope as

2x-36=6

and goes through the point (2, 3)

$$\begin{gathered} a. y=\frac{2}{3}x+\frac{5}{3} \\ b. y=\frac{2}{3}x \\ c. 2x+3y=6 \\ d. None of the above \end{gathered}$$

5. True or False

The set of points create a function

$A=\left\{\right(2,–3) (0,1), (5,–3), (–6,9\left)\right]$

6. Give the piecewise function

Evaluate the function at the specified input

f(4) = ______

7.  Given the graph, evaluate   ( f + g) ( 8 )

8.  Given the graph evaluate ( g o f) ( 0 )

$$\begin{gathered} a. 1 \\ b. –4 \\ c. Cannot determine the answer \\ d. None of the above \end{gathered}$$

9.  Given the two function

$$\begin{gathered} f\left(x\right) = \sqrt{x} \\ g\left(x\right) = x \end{gathered}$$

Determine the domain of the composite

$(g o f) \left(x\right)$

$$\begin{gathered} a. (–\infty ,\infty ) \\ b. (0,\infty ) \\ c. (–\infty ,0) \\ d. None of the above \end{gathered}$$

10.   Solve the supply and demand problem

The weekly demand and supply functions for a type of watch are given by

$$\begin{gathered} p=0.5x^2–2x+12 \\ p=0.5x^2+x+22 \end{gathered}$$

where p is measured in dollars, and x is measured in units of thousands.

Find the equilibrium quantity and price.

11. Evaluate

$li{m}_{x\to 3}\frac{x^2–3x}{x–3}$

12.  True or False

l

13.  Given the table determine

$li{m}_{x\to 0}f\left(x\right)$

$$\begin{gathered} a. \infty \\ b. –\infty \\ c. Does not exist \\ d. None of the above \end{gathered}$$

14.   True or False

Given the graph,

$li{m}_{x\to –2^{+}}f\left(x\right)=2$

15.  True or False

Given the graph the function is continuous at x = 1

16.  Find the derivative using the formal definition