Math Study Guide
Test 1
Solve each equation for x using any method learned in class.
(1) If there is no solution, then say so. Write your answers using complex numbers if needed.
Show/Explain your work.

(A) 20-3(x+4)=8-3x

(B)

(2)Solve each equation for x using algebra.
If there is no solution, then say so. Write your answers using complex numbers if needed.

(A)

(B)

(C)

(3) Simplify each of the following as much as possible.
Write your answers using complex numbers when needed.

(A) =____________

(B) =____________

(C) =_____________

(4) If the height (in feet) of a grapefruit thrown from the top of a building is
H(x) = feet, x seconds after it has been thrown.

(A) Evaluate H(6)=_____________

(B) Explain what the result of your answer to part (A) tells us in context to the problem.

(5) If f(x)= , then find the domain of f(x).
Domain: ________________

(6) If g(x)= , then find the domain of g(x).
Domain: _________________

(7) Given the following graph y=h(x), evaluate the following.
If there is no answer, then clearly say so.

(A) Evaluate h(3)= __________

(B) Evaluate h(-4)= ___________

(C) Evaluate where h(x)=4
Label your answer(s)

(D) Is y=h(x) the graph of a function? Explain

(8) Graph f(x)

(9) Toni sells cookies in her spare time. Each month she has to spend $200 on keeping up her kitchen as well as $4.25 per batch of cookies that she bakes. Write a function which models her monthly cost in terms of the number of batches of cookies she bakes.
Use correct function notation and be sure to clearly label your variables.

Test 2

(1) If f(x) = 3x-2 and g (x) -= +5, find the following
Simplify your answers if needed. If there is no solution, then say so.

(A) ()(4) = ___________

(B) () (4) = _____________

(C) (g-f)(x) + ______________

(D) (f of g)(x) +____________

(2) Suppose h(x)= . Find two functions f(x) and g(x) so that (f of g)(x) = h(x)

F(x) =________________

G(x) = ________________

(3) Suppose f(x) = m and g(x) = x-10.

(A) State the domain of (f + g) (x). Write your answer using interval notation.
Domain: __________________

(B) State the domain of (f of g) (x). Write your answer using interval notation.

Domain: _____________

(4) Suppose that U (x) = 2x-6 is the function which models the U.S. shirt size in terms of the Japanese shirt size of x. A(x) = 2x+8 is the function which models the Australian shirt size in terms of the U.S. shirt size of x.

(a) Find the U.S. shirt size given the Japanese shirt size of 10.

(b) Write the function which models the shirt sizes in Australia as a function of the shirt sizes in Japan. Be sure to clearly label the variable you used in your new function.

(5) If f(x) = find (X). Be sure to show all of your work

(x) = ___________

(6) Suppose the graph of g(x) is given below (it is the graph on the right)

(a) Sketch the graph of (x). Put your answer on the coordinate axis on the left.

(b) Is g(x) a one-to-one function? Explain.

(7) Given the following graph, identify a formula which defines this graph.

F(x) = _____________

(8) Write an equation which describes the graph of f(x) = which has been:
(i) Flipped over the y-axis.
(ii) Stretched vertically by a factor of 5.
(iii) Shifted left 10 units

Solution: ____________
(9) Write an equation which describes the graph of f(x) = which has been:
(i) Stretched horizontally by a factor of 2.
(ii) Shifted right 4 units.
(iii) Shifted up 7 units

Solution: ________________

(10) Write the formula of a quadratic function which has a vertex of (3,8) and which has a maximum value.

(11) Given g(x) = +62x+400
State the vertex of this parabola. Be sure to show/explain your work.

Test 3

(1) If f(x) = 8(x + 14) (2x (+4)
(a) Identify the real zeroes of f(x). If there are