Pre Calculus Honors Graded Assignment Semester 1
The final answer to 1 and 2 must be in standard polynomial form. You must do that work by hand.
1.
Create and graph a rational function that has all of the following attributes:
a. 2 vertical asymptotes---- 1 single rooted and 1 double rooted
b. A point/removable discontinuity located in quadrant 1
c. lim𝑥→∞ 𝑓(𝑥) = lim𝑥→−∞ 𝑓(𝑥) = 𝑦𝑜𝑢𝑟 𝑏𝑖𝑟𝑡ℎ 𝑚𝑜𝑛𝑡ℎ
d. You can have has many x intercepts as necessary
2.
Create and sketch the graph of a polynomial function that has all of the following attributes:
a. lim𝑥→∞ 𝑓(𝑥) = −∞
lim𝑥→−∞ 𝑓(𝑥) = ∞
b. 2 roots that are imaginary in the form a ± bi where a ≠0 and b ≠0
c. A positive value for y intercept
d. 1 root that is a positive even integer and 1 root that is a negative odd integer. No root = 0
e. Using your calculator find the coordinates of any relative extrema of your function.
3.
Create an absolute value function of the form f(x) = |𝑎𝑥 − 𝑏| + |𝑎𝑥 + 𝑏| where a = your birth month and
b = your birth day.
a. Define the function you created as a piecewise function.
b. Sketch the graph of the function
4.
Find the inverse of the function y = − 𝑏. Where a = your birth month and b = your birth day.
𝑎
𝑥
a. Find the domain and range of each function.
b. Sketch both the inverse and original function on the same graph in different colors.
5.
Write the equation of a horizontal hyperbola with center at( 1,2) and perpendicular asymptotes whose
constant difference is 2 times your birth month, by finding the values of a,b,c,h and k. Sketch the graph and label
the coordinates of the vertices and focal points.
6.
A rectangular box with square sides is made of 12 pieces of wire that have a total length of 48 inches.
Find the dimensions of the box that maximize the volume. What is the volume?
x
x
y
7. A simply supported beam is 64 feet wide. When a load is placed at the center of the beam the beam
deflects(bends) 1 inch to form a parabola.
a. Write the equation(using feet) of that parabola( place original center of beam at origin)
b. How far from the center of the beam is the deflection = ½ inch ?
No Load (Blue)
64 feet
8.
Load (Red)
origin
A satellite is orbiting the Earth in an elliptical path with the center of the Earth located at one focal
point. If the closest the satellite comes to the Earth’s surface is 1500 miles and the furthest it is from
the Earth’s surface is 6000 miles. Assuming the radius of the Earth is 4000 miles, write an ellipse
equation for the path round a,b,c to nearest integer.
Figure not drawn to scale
1500
6000
F1
9. Write and sketch a piecewise function with middle piece a quadratic, left piece an increasing linear
function and right piece a decreasing linear function. There can only be one jump discontinuity and no
other discontinuities.