MS 100 College Algebra Test seven • Name:

1. For the equation:
   $y=\frac{x^2}{8}-2x+16$
   1. [2] 16 Determine the y-intercept.
   2. [2] 8 - 8i, 8 + 8i Calculate the x-intercepts real or imaginary.
   3. [2] x = 8 Calculate the axis of symmetry.
   4. [2] (8,8) Calculate the coordinates of the vertex.
   5. [2] Yes Does the graph of the equation pass the vertical line test?
   6. [2] Yes Is the equation a function?
   7. [2] No Does the graph of the equation pass the horizontal line test?
   8. [2] No 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. [2] 5.2x − 25 Determine(f - g)(x)
   2. [2] −x² + 29x − 100 Determine (f × g)(x)
   3. [2] 0 Determine $(f\circ g)\left(5\right)$
   4. [2] −x + 5 Determine $(f\circ g)\left(x\right)=x$
   5. [2] Yes Does the function f(x) pass the vertical line test?
   6. [2] Yes Does the function f(x) pass the horizontal line test?
   7. [2] $f^{-1}\left(x\right)=\frac{(x+20)}{5}$ Determine the inverse function $f^{-1}\left(x\right)$
3. [2] 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 $v\left(f\right)=0.64f+0.81$. Lee Ling's speed per ball toss is given by:
   $(v\circ f)\left(b\right)=0.96b+0.81$

4. [1] parabola 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. [1] = −5/144 = −0.03472 = −45/1296
   2. [1] = −5/18 = −0.2778
   3. [1] = 400/9 = 44.44
6. [1] y = 400/9 = 44.44 Write the y-intercept for the graph depicted above.
7. [2] p = −7.2 [Alternately p = +7.2, distance is a magnitude.] Calculate the focus distance p for the parabola immediately above.
8. [4](−4,37.8) Calculate the coordinates of the focus.
9. [3 partial] Write out the standard form for the parabola immediately above.
   $(y-45)=\frac{-5}{144}{(x-(-4\left)\right)}^2$

10. For the graph seen above:
    1. [2] Yes Is the equation a function?
    2. [2] 4 What is the degree of the equation?
    3. [2] 4 How many zeros are there for the equation?
11. [3 partial] Find the standard form equation for the parabola formed by the shown focus and directrix:
    
    $(y-13.75)={1(x-6)}^2$
12. [3 all or nothing. Must clearly show correct values for x-intercepts, y-intercept.] 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.

    f(x)=x**6-34*x**4+225*x**2 
    %i1 expand((x-3)*(x+3)*(x-5)*(x+5)*x*x);
    %o1 x^6-34*x^4+225*x^2 
    

    

    1. [1] Yes Is the equation a function?
    2. [1] 6 What is the degree of the equation?
    3. [1] 6 How many zeros are there for the equation?
    4. [1] Use polynomial division to divide the equation by (x+3)
       x^5 − 3x^4 − 25x^3 + 75x^2
13. [3 all or nothing. Must clearly show correct values for x-intercepts, y-intercept. Must not violate x = ± vertical asymptotes.] 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. [1] −4 Determine the y-intercept for the rational function.
    2. [1] ±2 Determine the x-intercept(s) for the rational function.
    3. [1] ±7 Determine the vertical asymptotes for the rational function.
    4. [1] −7 < x < 7 Write out the domain for the rational function.