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college algebra
Questions and Answers of
College Algebra
Decide whether or not each equation has a circle as its graph. If it does, give the center and radius. If it does not, describe the graph.x2 + y2 - 6x - 6y + 18 = 0
Decide whether each relation defines y as a function of x. Give the domain and range.x = y6
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (- 5/2, 3), undefined slope.
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = √x - 2, g(x) = 2x
Graph each function.ƒ(x) = x2 - 2
Use a graphing calculator to graph each equation in the standard viewing window.y = -2x + 3
Use the graph to evaluate each expression.(a) (ƒ + g)(1) (b) (ƒ - g)(0)(c) (ƒg)(-1) (d) (ƒ/g)(1) 3. y = g(x) y = f(x)}
Suppose the point (8, 12) is on the graph of y = ƒ(x).Find a point on the graph of(a) y = 1/4 ƒ(x) (b) y = 4ƒ(x).
Find the slope and y-intercept of each line, and graph it.y = -2x + 7
Let ƒ(x) = -2x2 + 3x - 6. Find each of the following.ƒ(k)
Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint.Midpoint (-7, 6), endpoint (-9, 9)
Give a rule for each piecewise-defined function. Also give the domain and range. y х
Decide whether or not each equation has a circle as its graph. If it does, give the center and radius. If it does not, describe the graph.x2 + y2 + 4x + 4y + 8 = 0
Decide whether each relation defines y as a function of x. Give the domain and range.x = y4
Use a graphing calculator to graph each equation in the standard viewing window.3x + 4y = 6
Use the table to evaluate each expression in parts (a)–(d), if possible.(a) (ƒ + g)(2) (b) (ƒ - g)(4) (c) (ƒg)(-2) (d) (ƒ/g)(0) f(x) g(x) -2 6. -2 4 10
Suppose the point (8, 12) is on the graph of y = ƒ(x).Find a point on the graph of(a) y = ƒ(4x) (b) y = ƒ (1/4 x).
Find the slope and y-intercept of each line, and graph it.4x - y = 7
Graph each equation.2x - 5y = 5
Give a rule for each piecewise-defined function. Also give the domain and range. 2 -2 2.
Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint.Midpoint (12, 6), endpoint (19, 16)
Decide whether or not each equation has a circle as its graph. If it does, give the center and radius. If it does not, describe the graph.9x2 + 9y2 - 6x + 6y - 23 = 0
Decide whether each relation defines y as a function of x. Give the domain and range.y = 2x - 5
Use a graphing calculator to graph each equation in the standard viewing window.-2x + 5y = 10
Use the table to evaluate each expression in parts (a)–(d), if possible.(a) (ƒ + g)(2) (b) (ƒ - g)(4) (c) (ƒg)(-2) (d) (ƒ/g)(0) f(x) g(x) х -4 -2 -1 4 4 2.
For each line, (a) find the slope and (b) sketch the graph.2y = -3x
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y = Vx - 3
The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.A circle has a diameter with endpoints (-1, 3) and (5, -9).
Let ƒ(x) = 2x - 3 and g(x) = -x + 3.(ƒ ° g)(4)
The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.A circle has a diameter with endpoints (-1, 3) and (5, -9).
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(ƒ ° g)(2)
Graph each function.ƒ(x) = x2 - 1
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(ƒ ° g)(-2)
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (-2, -3), m = - 3/4
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(g º ƒ)(3)
Answer the following.If the point (a, b) is in the second quadrant, then in what quadrant is (a, -b)? (-a, b)? (-a, -b)? (b, a)?
Graph each function.ƒ(x) = x2 + 2
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(g º ƒ)(0)
Graph each function.ƒ(x) = x2 + 3
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(g º ƒ)(-2)
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(ƒ ° ƒ)(2)
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.ƒ (a + 4)
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.x-intercept (-3, 0), y-intercept (0, 5)
Answer the following.Find the coordinates of the points that divide the line segment joining (4, 5) and (10, 14) into three equal parts.
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (9/4, 2), undefined slope
Graph each function.g(x) = (x - 2)2
Let ƒ(x) = 2x - 3 and g(x) = -x + 3. Find each function value.(g ° g)(-2)
When the Celsius temperature is 0°, the corresponding Fahrenheit temperature is 32°. When the Celsius temperature is 100°, the corresponding Fahrenheit temperature is 212°. Let C represent the
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.f (2m - 3)
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (2, -10), perpendicular to a line with undefined slope
Find and interpret the average rate of change illustrated in each graph. 16 12 4 2 3 Year Value of Machine (in thousands of dollars)
The tables give some selected ordered pairs for functions ƒ and g.Find each of the following.(ƒ ° g)(2) 3 4 1 f(x) 1 g(x) 3 12 3 6. 2. 3.
Graph each function.g(x) = (x + 2)2
The pressure P of water on a diver’s body is a linear function of the diver’s depth, x. At the water’s surface, the pressure is 1 atmosphere. At a depth of 100 ft, the pressure is about 3.92
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.f (3t - 2)
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (0, 5), perpendicular to 8x + 5y = 3
Find and interpret the average rate of change illustrated in each graph. y х 3 4 Month Amount Saved (in dollars) 2.
The tables give some selected ordered pairs for functions ƒ and g.Find each of the following.(ƒ ° g)(7) 3 4 1 f(x) 1 g(x) 3 12 3 6. 2. 3.
Graph each function.g(x) = (x + 3)2
In Keynesian macroeconomic theory, total consumption expenditure on goods and services, C, is assumed to be a linear function of national personal income, I. The table gives the values of C and I for
For each function, find (a) ƒ(2) and (b) ƒ(-1).ƒ = {(-1, 3), (4, 7), (0, 6), (2, 2)}
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (-7, 4), perpendicular to y = 8
Find and interpret the average rate of change illustrated in each graph. 4 Year 3. 2. 4- 2. Percent of Pay Raise
The tables give some selected ordered pairs for functions ƒ and g.Find each of the following.(g ° ƒ)(3) 3 4 1 f(x) 1 g(x) 3 12 3 6. 2. 3.
Graph each function.g(x) = |x| - 1
A graph of y = ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) = 0?A. -15 B. 0 C. 5 D. 15 HORTAL
For each function, find (a) ƒ(2) and (b) ƒ(-1).f = {(2, 5), (3, 9), (-1, 11), (5, 3)}
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (3, -5), parallel to y = 4
Find and interpret the average rate of change illustrated in each graph. 20 15 10 5 3 Year Number of Named Hurricanes 2.
The tables give some selected ordered pairs for functions ƒ and g.Find each of the following.(g ° ƒ)(6) 3 4 1 f(x) 1 g(x) 3 12 3 6. 2. 3.
Graph each function.g(x) = |x + 3| + 2
Use a graphing calculator to solve each linear equation.2x + 7 - x = 4x - 2
For each function, find (a) ƒ(2) and (b) ƒ(-1). -1 -10 2- -15 19 27 5-
Graph each function.ƒ(x) = |x| - 3
Solve each problem.In 1980, the number of high school dropouts in the United States was 5085 thousand. By 2012, this number had decreased to 2562 thousand. Find and interpret the average rate of
The tables give some selected ordered pairs for functions ƒ and g.Find each of the following.(ƒ ° ƒ)(4) 3 4 1 f(x) 1 g(x) 3 12 3 6. 2. 3.
Graph each function.h(x) = -(x + 1)3
For each function, find (a) ƒ(2) and (b) ƒ(-1). 2- -1 3- -20
Graph each function.ƒ(x) = - |x|
Solve each problem.The total amount spent on plasma flat-panel TVs in the United States changed from $5302 million in 2006 to $1709 million in 2013. Find and interpret the average rate of change in
The tables give some selected ordered pairs for functions ƒ and g.Find each of the following.(g ° g)(1) 3 4 1 f(x) 1 g(x) 3 12 3 6. 2. 3.
Graph each function.h(x) = -(x - 1)3
Use a graphing calculator to solve each linear equation.3(2x + 1) - 2(x - 2) = 5
For each function, find (a) ƒ(2) and (b) ƒ(-1). .4 2 |-2 0 2. = f(x).
Graph each function.ƒ(x) = -(x + 1)2 + 3
The graph shows the winning times (in minutes) at the Olympic Games for the men’s 5000-m run, together with a linear approximation of the data.Olympic Times for 5000-Meter Run (in minutes)(a) An
Why can we not determine (ƒ ° g)(1) given the information in the tables for Exercises
Graph each function.h(x) = 2x2 - 1
Use a graphing calculator to solve each linear equation.4x - 3(4 - 2x) = 2(x - 3) + 6x + 2
For each function, find (a) ƒ(2) and (b) ƒ(-1). y = f(x)
Graph each function.ƒ(x) = -√x - 2
The graph shows the number of U.S. radio stations on the air, along with the graph of a linear function that models the data.U.S. Radio Stations(a) An equation for a linear model, based on data from
Extend the concept of composition of functions to evaluate (g ° (ƒ ° g))(7) using the tables for Exercises
Graph each function.h(x) = 3x2 - 2
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2), (b) ƒ(0), (c) ƒ(1), and (d) ƒ(4). II 12+3-4 -2–1-0 ttt2 IN
Use a graphing calculator to solve each linear equation.(a) Solve -21x - 52 = -x - 2 using traditional paper-and-pencil methods.(b) Explain why the standard viewing window of a graphing calculator
Graph each function.ƒ(x) = [[x - 3]]
The table gives the number of cellular telephone subscribers in the U.S. (in thousands) from 2008 through 2013. Find the average annual rate of change during this time period. Round to the nearest
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = -6x + 9, g(x) = 5x + 7
Graph each function.ƒ(x) = 2(x - 2)2 - 4
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