Reference no: EM131007663
1) Determine if the following relation represents a function. If the relation is a function, then state its domain and range.
{(2, 3), (4, 3), (3, 3), (2, -1)}
2) For the function f defined by f(x) = -3x2 + 2x, evaluate:
(a) f(-x)
(b) f(x+3)
3) Find the domain and range of the function y = f(x) = -x2 + 5.
4) For the function f(x)= 2x - 4 and g(x) = -3x + 6, find the following.
(a) (f+ g)(x)
(b) (f + g) (1)
5) Is the following graph a of function? In either case, state the domain and range of the relation.
6) Obtain information from or About the Graph of a Function.
(a) What is the domain of f?
(b) What is the range of f?
(c) How often does the line y = 2 intersect the graph?
(d) For what values of x is f(x) = 4?
7) Use the definitions of even and odd functions to determine algebraically whether the following function is even, odd, or neither.
g(x) = x3 - 1
8) Determine the following from the graph below:
(a) Where is the function increasing?
(b) Where is the function constant?
9) Suppose that g(x) = -2x2 + 4x - 3. Find the average rate of change of g from -2 to x.
10) The function f is defined as-
(a) Determine the domain of f.
(b) Graph f.
(c) Use the graph to find the range of f.
(d) Is f continuous on its domain?
11) Use the graph of f(x) = |x| to obtain the graph of g(x) - -2|x+1| - 3.
12) Suppose that a company just purchased some now office equipment at a cost of $2500 per machine. The company chosen to depreciate each machine using the straight-line method over 5 years, this means that each piece of equipment will depreciate by $2500/5 = $500 per year.
(a) Build a linear model that expresses the value V of each machine as a function of its age, x.
(b) What is the implied domain of the function in (a)?
(c) What is the value of each machine after 2 years?
(d) Interpret the slope.
(e) When will the value of each machine be $500?
13) Graph f(x) = -2x2 + 6x + 2 onto the grid using transformations. (Write into vertex form and show transformations).
14) Without graphing, locate the vertex and axis of symmetry of the parabola defined by f(x) = -3x2 + 6x + 1. Does it up or down?
15) Graph f(x) = -x2 + 4x - 7 by determining whether the graph opens up or down and finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.
16) Solve the inequality x2 + 3x - 28 > 0.
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