MS 100 College Algebra Test Four

1. Blast from the past. 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 $(k\circ v)\left(d\right)$