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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Use the graph of y = Cax to determine values for C and a. 3 3
Find f-1(x). f(x) = 1 x+5 +2
Solve each equation. Use the change of base formula to approximate exact answers to the nearest hundredth when appropriate.
Use the graph of y = Cax to determine values for C and a. 5 3
Use properties of logarithms to combine the expression as a logarithm of a single expression. log V3 - log V3
Find the domain of (f ° g)(x) and (g ° f)(x). f(x) = lnx, g(x)=√x-1
Use the graph of y = Cax to determine values for C and a. -2 -1 -8 12
Find f-1(x). ² = (x) f 1- I
Solve each equation. Use the change of base formula to approximate exact answers to the nearest hundredth when appropriate. 105 95 =
Find the domain of (f ° g)(x) and (g ° f)(x). f(x) = lnx, g(x) = 1 - e
Expand In y/x2
Expand log (4x3/k).
Use the graph of y = Cax to determine values for C and a. 12 X
Find the domain of (f ° g)(x) and (g ° f)(x). f(x) = 2x, g(x) = log(-x)
Find f-1(x). f(x) 2 2-x
Solve each equation. Use the change of base formula to approximate exact answers to the nearest hundredth when appropriate. 2-10⁰ = 66
Restrict the domain of f(x) so that f is one-to-one. Then find f-1(x). f(x) = 4-x²
Solve each equation. Use the change of base formula to approximate exact answers to the nearest hundredth when appropriate. 10³ = 100
The equations are identities because they are true for all real numbers. Use properties of logarithms to simplify the expression on the left side of the equation so that it equals the expression on
Match the equation with its graph (a-d). ,
Sketch a graph of the ellipse. (x + 2)² 4 + y² = 1
Find an (approximate) equation of the hyperbola shown in the graph. Identify the vertices, foci, and asymptotes. 12
Sketch a graph of the ellipse. (x-4)² 9 4
Find an (approximate) equation of the hyperbola shown in the graph. Identify the vertices, foci, and asymptotes. 5 X
Sketch a graph of the ellipse. x² + (y - 3)² 4 1
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions. Focus (0, -1)
A comet travels along an elliptical orbit around the sun. Its path can be described by the equationwhere units are in millions of miles. (a) What are the comet's minimum and maximum distances from
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the vertices and foci. (x-1)² 4 (y-1)² 4 = 1
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions.Directrix x = 1/4
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions.Focus (-1,0)
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions.Focus (1, 0)
Match the equation with its graph (a-d). (x - 2)² (y + 4)² 16 36 1
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions.Directrix y = -1
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the vertices and foci. y2. (x - 2)² 4 1
Match the equation with its graph (a-d). 25 (y + 1)² 10 1
Sketch a graph of the ellipse. Identify the foci and vertices. (x - 1)² (y-1)² 9 25 1
Find the standard equation of a hyperbola with center (h, k) that satisfies the given conditions. Vertices (-1, ±1) and foci (-1, ±3)
Sketch a graph of the ellipse. Identify the foci and vertices. (x + 2)² (y + 1)² + 25 16 = 1
Sketch a graph of the ellipse. Identify the foci and vertices. 뭐요 4 (y - 1)² 9 = 1
Sketch a graph of the ellipse. Identify the foci and vertices. (x + 4)² 16 (y-2)² 9 = 1
Find the standard equation of a hyperbola with center (h, k) that satisfies the given conditions. Vertices (2 ± 1, 1) and foci (2 ± 3,1)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. x²-2x = y² + 2y = 4
Find the standard equation of a hyperbola with center (h, k) that satisfies the given conditions.Center (-1, 1), focus (-1, 4), and vertex (-1,3)
Find an equation of an ellipse that satisfies the given conditions. Center (2, 1), focus (2, 3), and vertex (2, 4)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. 9 = x + ₂x + + ₂
Find an equation of a parabola that satisfies the given conditions.Focus (0, -3) and directrix y = 3
Find an equation of an ellipse that satisfies the given conditions. Center (-3,-2), focus (-1, -2), and vertex (1, -2)
Sketch a graph of the parabola. (x - 2)² = −(y + 1)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. 3y² + 24y= 2x² + 12x + 24 = 0
Sketch a graph of the parabola. (x - 1)² = (y-2)
Find an equation of an ellipse that satisfies the given conditions. Vertices (±3, 2) and foci (±2, 2)
Find an equation of a parabola that satisfies the given conditions.Focus (0, 2) and directrix y = -2
Sketch a graph of the parabola. (y-1)² = (x + 1)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. 4x² + 16x9y² + 18y = 29
Find an equation of a parabola that satisfies the given conditions.Focus (-1,0) and directrix x = 1
Find an equation of an ellipse that satisfies the given conditions. Vertices (-1, ±3) and foci (-1, ±1)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. y² + 8y = 3x² + 13 = 0
Find an equation of a parabola that satisfies the given conditions.Focus (3, 0) and directrix x = -3
Find an (approximate) equation of the ellipse shown in the figure. -2 6 2 6 X
Sketch a graph of the parabola. (y + 2)² = 2x
Find an (approximate) equation of the ellipse shown in the figure. 3
Match the equation with its graph (a-d). (x - 1)² = 4(y - 1)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. 41² + + 32y 5x² - 10x + 39 = 0
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. y² + 8y = 3x² + 13 = 0
Graph the parabola. Label the vertex, focus, and directrix. (x - 2)² = 8(y + 2)
Write the standard form for a hyperbola centered at (h, k). Identify the center and the vertices. 5x² + 10x - 7y² + 28y = 58
Match the equation with its graph (a-d). (x + 1)² = -4(y-2)
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 9x²36x + 16y²-64y - 44 = 0
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 9x² + 18x + 4y²-8y - 23 = 0
Match the equation with its graph (a-d). (y + 1)² = 8(x + 3)
Match the equation with its graph (a-d). (y-2)² = -8x
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 4x² + 8x + y² + 2y + 1 = 0
Graph the parabola. Label the vertex, focus, and directrix. (x + 4) = −(y − 4)
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 4x² + 16x + 5y² − 10y + 1 = 0 -
Graph the parabola. Label the vertex, focus, and directrix. x = − (y + 3)² + 2
Graph the parabola. Label the vertex, focus, and directrix. x = 2(y-2)² - 1
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 4x² + 16x + 5y² - 10y + 1 = 0
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 16x²16x + 4y² +12y = 51
Graph the parabola. Label the vertex, focus, and directrix. y = = (x + 2)² -
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 2x² + 4x + 3x² − 18y + 23 = 0
Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. 16x² + 48x + 4y² - 20y + 57 = 0
Graph the parabola. Label the vertex, focus, and directrix. -2(y + 1) = (x + 3)²
Write the equation in standard form for a circle centered at (h. k). Identify the center and the radius. x² + 6x + y² + 4y - 23 = 0
Write the equation in standard form for a circle centered at (h. k). Identify the center and the radius. x² + 2x + y² + 6y + 5 = 0
Write the equation in standard form for a circle centered at (h. k). Identify the center and the radius. x²8x + y² - 2y + 8 = 0
Write the equation in standard form for a circle centered at (h. k). Identify the center and the radius. x² + 10x + y² - 10y + 34 = 0
Write the equation in standard form for a circle centered at (h. k). Identify the center and the radius. x - 2x + y + 8y - 32 = 0
Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex.Focus (0, 2) and vertex (0, 1)
Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex.Focus (-1, 2) and vertex (3, 2)
Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex.Focus (0,0) and directrix x = -2
Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex.Focus (2, 1) and directrix x=-1
Write the given equation in either the form (yk)² = a (x - h) or (xh)² = a(y-k).
Write the given equation in either the form (yk)² = a (x - h) or (xh)² = a(y-k).
Write the equation in standard form for a circle centered at (h. k). Identify the center and the radius. x² - 6x + y²-8y + 21 = 0
Write the given equation in either the form (yk)² = a (x - h) or (xh)² = a(y-k).
Write the given equation in either the form (yk)² = a (x - h) or (xh)² = a(y-k).
Solve the system of equations. Give graphical support by making a sketch. 4x² + 16y² = 64 x² + y² = 9
Solve the system of equations. Give graphical support by making a sketch. 4 = 1 9 x+y = 3
Write the given equation in either the form (yk)² = a (x - h) or (xh)² = a(y-k).
Find an equation of a parabola that satisfies the given conditions.Focus (-1, 3) and directrix y = 7

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