MS 100 College Algebra Test seven • Name:

1. For the equation:
   $y=\frac{x^2}{8}-2x+16$
   1. __________ Determine the y-intercept.
   2. __________ __________ Calculate the x-intercepts real or imaginary.
   3. x = __________ Calculate the axis of symmetry.
   4. (________,_______) Calculate the coordinates of 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. _________________________ Determine(f - g)(x)
   2. _________________________ Determine (f × g)(x)
   3. _________________________ Determine $(f\circ g)\left(5\right)$
   4. _________________________ Determine $(f\circ g)\left(x\right)=x$
   5. __________ Does the function f(x) pass the vertical line test?
   6. __________ Does the function f(x) pass the horizontal line test?
   7. _________________________ Determine the inverse function $f^{-1}\left(x\right)$
3. For a running juggler (a joggler) ball tosses are necessarily in synchronization with the movement of their legs. The time aloft for a ball is proportional to the toss height. A lower toss lands sooner, and one has to juggle faster. Thus for a joggler to go faster, he or she only has to toss the balls lower. This drives the legs faster, which increases the speed. The number of footfalls f per second for a given ball toss rateb is given by $f\left(b\right)=1.5b$. Lee Ling's speed (velocity) v as a function of his footfalls f per second is given by $v\left(f\right)=0.64f+0.81$. Determine Lee Ling's speed per ball toss by completing the composition $(v\circ f)\left(b\right)$

4. _______________ What is the name of the shape seen on the graph below?

Data table for the above graph

5. Calculate 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 = ___________ Write the y-intercept for the graph depicted above.
7. p = ___________ Calculate the focus distance p for the parabola immediately above.
8. (____________,__________) Calculate the coordinates of the focus.
9. Write out the standard form for the parabola immediately above.
   $(y-\text{\_\_\_\_\_\_\_\_\_})={\text{\_\_\_\_\_\_\_\_\_}(x-\text{\_\_\_\_\_\_\_\_\_})}^2$

10. For the graph seen above:
    1. _________ Is the equation a function?
    2. _________ What is the degree of the equation?
    3. _________ How many zeros are there for the equation?
11. Find the standard form equation for the parabola formed by the shown focus and directrix:
    
    $(y-\text{\_\_\_\_\_\_\_\_\_})={\text{\_\_\_\_\_\_\_\_\_}(x-\text{\_\_\_\_\_\_\_\_\_})}^2$
12. 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)
13. 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.