MS 100 College Algebra Preview

16 July 2008

1. For the equation:
   $y=\frac{x^2}{8}-2x+16$
   1. __________ Find the y-intercept.
   2. __________ Find the x-intercepts real or imaginary.
   3. __________ Find the axis of symmetry.
   4. __________ Find the vertex.
   5. __________ Does the graph of the equation pass the vertical line test?
   6. __________ Is the equation a function?
   7. __________ Does the graph of the equation pass the horizontal line test?
   8. __________ Does the equation as written have an inverse function?
2. For the following questions use the following functions:
   f(x) = 5x − 20
   g(x) = −0.20x + 5
   
   1. _________________________ Find $(f\circ g)\left(5\right)$
   2. _________________________ Find $(g\circ f)(-5)$
   3. _________________________ Find (f + g)(x)
   4. _________________________ Find (f - g)(x)
   5. _________________________ Find (f × g)(x)
   6. _________________________ Find [g(x)]²
   7. _________________________ Find $(f\circ g)\left(x\right)=x$
   8. _________________________ Find $(g\circ f)\left(x\right)=x$
   9. __________ Does the function f(x) pass the vertical line test?
   10. __________ Does the function f(x) pass the horizontal line test?
   11. _________________________ Find the inverse function $f^{-1}\left(x\right)$
   12. __________ Does the function g(x) pass the vertical line test?
   13. __________ Does the function g(x) pass the horizontal line test?
   14. _________________________ Find the inverse function $g^{-1}\left(x\right)$
3. A water wave in shallow water travels with a velocity $v=\sqrt{gd}$ where g is the acceleration of gravity and d is the depth of the water. The kinetic energy of a moving object is k(v) = $\frac{1}{2}m{v}^2$where m is the mass and v is the velocity. Find $(k\circ v)\left(d\right)$
4. _______________ What is the name of the shape seen on the graph below?

Data table for the above graph

5. Find a, b, and c in the y = ax² + bx + c form of the equation for the graph above. The coordinates for both x-intercepts and the vertex are depicted on the graph.
   1. = __________
   2. = __________
   3. = __________
6. y = ___________ Find the y-intercept for the graph depicted above.
7. Use a Qalculate! to help you sketch a graph of $\text{f(x)}=x^6-34x^4+225x^2$ over the domain −5.1 ≤ x ≤ 5.1. Sketch the graph on your paper.
   1. _________ Is the equation a function?
   2. _________ What is the degree of the equation?
   3. _________ How many zeros are there for the equation?
   4. Use polynomial division to divide the equation by (x+3)

Data table for the above parabola

9. Find a, b, and c in the y = ax² + bx + c form of the equation for the graph above. The coordinates for both x-intercepts and the vertex are depicted on the graph.
   1. = __________
   2. = __________
   3. = __________
10. y = ___________ Find the y-intercept for the parabola immediately above.
11. p = ___________ Find the focus distance p for the parabola immediately above.
12. Write out the standard form for the parabola immediately above.
    $(y-\text{\_\_\_\_\_\_\_\_\_})={\text{\_\_\_\_\_\_\_\_\_}(x-\text{\_\_\_\_\_\_\_\_\_})}^2$
13. Given that $a=\frac{1}{4p}$, determine the focal distance p for y = 0.025x² + 8.2x + 16.4
14. Use a Qalculate! to help you sketch a graph of $\text{f(x)}=\frac{7x^2-28}{\sqrt{(49-x^2)}}$ Sketch the graph on your paper.
    1. _________ Determine the y-intercept for the rational function.
    2. ___________________________ Determine the x-intercept(s) for the rational function.
    3. __________________ Determine the vertical asymptotes for the rational function.
    4. __________________ Write out the domain for the rational function.
15. Find the standard form equation for the parabola formed by the shown focus and directrix: