College Algebra
Improve your experience by picking them
Graph the following equations on one Cartesian coordinate plane and describe the effect of the coefficient of x² on the graph's appearance:
y = x2, y = 5x2, y = 1/5x2
For the following function, graph and identify its domain's open intervals for which the function is increasing or decreasing. f(x) = 7x4
For the following function, graph and identify its domain's open intervals for which the function is increasing or decreasing. f(x) = (1/5)(x + 5)4 - 5
For the following function, graph and identify its domain's open intervals for which the function is increasing or decreasing. (1/5)(x - 5)2 + 3
For the following polynomial function, graph. f(x) = - 3x(x - 4)(x + 1)
For the following polynomial function, graph. f(x) = - x(x + 3)(x - 3)
Consider the function f(x) = (x + 8)2 and find the largest open interval of the domain at which the function is increasing and decreasing.
Consider the function f(x) = -(x - 4)2 + 6 and find the largest open interval of the domain at which the function is increasing and decreasing.
Consider the function f(x) = x2 + 12x + 40 and find the largest open interval of the domain at which the function is increasing and decreasing.
Consider the function f(x) = -2x2 + 12x - 23 and find the largest open interval of the domain at which the function is increasing and decreasing.
For the following polynomial function, graph. f(x) = x2(x - 2)(x + 2)(x - 7)
For the following polynomial function, graph. f(x) = (5x - 2)(x + 1)2
For the following polynomial function, graph. f(x) = (2x + 5)(x + 1)2
For the following polynomial function, graph. f(x) = x3 + 2x2 - 9x - 18
For the following polynomial function, graph. f(x) = - x3 + 2x2 + 15x
For the following polynomial function, graph. f(x) = 6x3(x2 - 1)(x - 2)
For the following polynomial function, determine whether the real zero satisfies the given condition or not.
f(x) = x4 - 3x3 + 6x2 - 12x + 10; no real zero greater than 3
f(x) = 4x5 - 3x4 + 5x3 - 7x2 + 12x - 11; no real zero greater than 4
f(x) = 2x4 + 3x3 - 6x2 + 7; no real zero less than -4
f(x) = 3x5 + 5x3 - 7x2 + 2x + 9; no real zero less than -5
Determine the end behavior of the graph of the following function:
f(x) = 4x5 -3x3 + x2 - 2x + 12
f(x) = -3x3 + 7x2 + 13x - 15
f(x) = -10x5 + 9x2 - 17
f(x) = 8x5 - 2x4 + 9x3 - 21
f(x) = 11x8 - 4x6 + 7x2 - 13
f(x) = 5 + 7x - 27x2 - 13x12
For the following polynomial function, graph. f(x) = 4x3 + 3x2 - 9x + 2
f(x) = 14 + x - 3x2 + 9x3 - 16x4
For the graph given below, find a polynomial function f(x) of minimum degree.
For the following polynomial function with a specified domain, determine the coordinates of the turning point with the help of a graphing utility. Round your answer to the nearest hundredth.
f(x) = 4x3 - 7x2 - 8x + 2; [-1, 1]
f(x) = x3 + 2x2 - 11x - 5; [-3.4, -2]
f(x) = x4 - 11x3 + 19x2 + 21x - 19; [-0.8, 0.1]
A certain polynomial function has the following leading term: 20x9
Based on this leading term, infer the following features of its graph: (1) domain (2) range (3) end behavior (4) no. of zeros (5) no. of turning points
A certain polynomial function has the following leading term: - 13x8
Based on this leading term, infer the following features of its graph:(1) domain (2) range (3) end behavior (4) no. of zeros (5) no. of turning points
A cardboard has a dimension of 100 cm by 70 cm. This will be turned into a storage box by cutting squares from each of its corners and folding up its sides. The squares will be of the same dimensions. Let x be the length, in centimeters, of the side of each square to be cut. Determine the value of x that will maximize the volume of the storage box by using the table feature of a graphing utility. Express your answer in two decimal places.
One leg of a right-angle triangle is 7 units lesser than the hypotenuse. If the area of the triangle is 30 square units and we consider the length of the hypotenuse as x, provide the length of the leg in terms of x and also find the domain.
Express that the given function has a real zero between the x-values 12 and 14 using the intermediate value theorem.
ƒ(x)=x2 -19x +78
Express that the given function has a real zero between the numbers given using the intermediate value theorem.ƒ(x)=-4x3 + 9x2 +2x -1; 0 and 2
Express that the given function has a real zero between the x-values 1 and 3 using the intermediate value theorem.
ƒ(x)= 9x4 -3x2 +3x -10
Consider the given polynomial function and plot its graph.ƒ(x)=(x -9)2(x+13)
Consider the given polynomial function and plot its graph.ƒ(x) = 7x3 +20x2 -3x
Consider the given polynomial function and plot its graph.ƒ(x) = -17x4 +304x3 -1341x2 -162x
Consider the given polynomial function and plot its graph.ƒ(x)=(x-17)2(x-29)
Consider the given polynomial function and plot its graph.
ƒ(x) = -(x-17)2(x-29)
Consider the given polynomial function and plot its graph.ƒ(x) = (x-17)2(x-29)2
Consider the given polynomial function and plot its graph. ƒ(x) = (x-17)(x-29)
Consider the given polynomial function and plot its graph. ƒ(x) = -(x-17)(x-29)
ƒ(x) = -(x-17)2(x-29)2
In the graph of f(x) = 3x4 -29x3 +105x2 -213x +190, two real zeroes are displayed. Determine the remaining nonreal roots.
Determine whether the graph shown represents a polynomial function.
Express the following polynomial in decreasing powers of x: 9 + 2x - 5x2 - 9x3
Use the following equation to factor 2x3 + 4x2 - 26x + 20:
(2x3 + 4x2 - 26x + 20)/(x - 1) = 2x2 + 6x - 20
Determine if the following function is a polynomial or not. If it is, what is its degree?
f(x) = 2x2 + 9x4
f(x) = 3x4 - πx2 + (2/7)x
f(x) = 9x5 + 5x4 + 3/x
f(x) = x1/5 - 5x6 + 1
f(x) = (x3 + 8)/x5
f(x) = (x3 + 8)/9
For the following polynomial function, use the Leading Coefficient Test to determine the end behavior of the graph and sketch the graph of the function.
f(x) = -7x3 + 2x2 - 4x
f(x) = 2x6 + 3x4 - 5x2 + 1
Graph the given function: f(x) = x3 + 2x2 - 3x - 4(i) Determine the graph's end behavior using the Leading Coefficient Test(ii) Determine if it has y-axis symmetry, origin symmetry, or neither(iii) Graph
Determine the end behavior of the graph of the following polynomial function using the Leading Coefficient Test: f(x) = 7x3 + 2x2 - 3x + 11
Graph the given function.(i) Determine the graph's end behavior using the Leading Coefficient Test(ii) Determine if it has y-axis symmetry, origin symmetry, or neither(iii) Graphf(x) = - 2x(2x2 - 3)
Determine the end behavior of the graph of the following polynomial function using the Leading Coefficient Test: f(x) = 3x4 - 3x2 - x + 5
Determine the end behavior of the graph of the following polynomial function using the Leading Coefficient Test: f(x) = -9x4 + 9x2 + 2x + 11
Graph the given polynomial expression. f(x) = x2(x + 1)3(x - 2)
Identify the zeros of the given polynomial function and state their multiplicities. Describe also how the graph behaves with the x-axis.
f(x) = 5(x - 3)(x + 6)2
f(x) = 5(x + 6)(x + 8)2
Graph the given polynomial function. f(x) = -(1/2)x3(x + 3)2(2x - 2)
f(x) = -7(x + 3/5)(x - 9)3
f(x) = x3 + 8x2 - 9x - 72
Justify that the polynomial f(x) = x3 + 4x - 3 has a real zero in between 0 and 1 by using the Intermediate Value Theorem.
Justify that the polynomial f(x) = 2x3 - 8x2 + 4 has a real zero in between -1 and 0 by using the Intermediate Value Theorem.
Justify that the polynomial f(x) = 2x4 + 5x3 - 9x2 has a real zero in between 1 and 2 by using the Intermediate Value Theorem.
Justify that the polynomial f(x) = 2x3 + 4x2 - 6x + 3 has a real zero in between -4 and -3 by using the Intermediate Value Theorem.
Justify that the polynomial f(x) = 5x3 - 3x2 + 2x + 1 has a real zero in between -1 and 0 by using the Intermediate Value Theorem.
Factor completely:
x3 + 4x2 -25x - 100
Consider the following function: f(x) = 4x4 - 7x2 + 1
Determine if it is even, odd, or neither; and describe the symmetry, if any.