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7. Describe the graphs of the following equations. Include a rough sketch of the basic shape of the graph. A) y = -2sin(x) +3 B) y = (x - 1)³

7. Describe the graphs of the following equations. Include a rough sketch of the basic shape of the graph. A) y = -2sin(x) +3 B) y = (x - 1)³

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 47E
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7. Describe the graphs of the following equations. Include a rough sketch of the basic shape of the graph. A) y = -2sin(x) + 3 B) y = (x - 1)³ 8. What type of discontinuity does the function f(x) = x²-x-12 have at x = 4? If it is a removable x-4 discontinuity, how could you define a function such that it would be continuous at x = 4? 10. Given the graph shown: A) Sketch the secant line between x = 1 and x = 4. Estimate the slope of this secant line. slope B) Sketch a tangent line at x = 1. Estimate the slope of the tangent line. slope 11. A) Find the slope of the tangent line to the curve f(x) = x² + 5x at x = 3 using a definition of the derivative. Definition: The tangent line to the curve y=f(x) at the point P(a, f(a)) is the line through P with slope m = limf(x)-f(a) provided the limit exists. (NOT PROVIDED ON THE TEST!) x-a m = lim h→0 f(a+h)-f(a) h or m = lim x→a f(x)-f(a) x-a B) Find the equation of the tangent line to the curve f(x) = x² + 5x at x = 3. x→a
Transcribed Image Text:7. Describe the graphs of the following equations. Include a rough sketch of the basic shape of the graph. A) y = -2sin(x) + 3 B) y = (x - 1)³ 8. What type of discontinuity does the function f(x) = x²-x-12 have at x = 4? If it is a removable x-4 discontinuity, how could you define a function such that it would be continuous at x = 4? 10. Given the graph shown: A) Sketch the secant line between x = 1 and x = 4. Estimate the slope of this secant line. slope B) Sketch a tangent line at x = 1. Estimate the slope of the tangent line. slope 11. A) Find the slope of the tangent line to the curve f(x) = x² + 5x at x = 3 using a definition of the derivative. Definition: The tangent line to the curve y=f(x) at the point P(a, f(a)) is the line through P with slope m = limf(x)-f(a) provided the limit exists. (NOT PROVIDED ON THE TEST!) x-a m = lim h→0 f(a+h)-f(a) h or m = lim x→a f(x)-f(a) x-a B) Find the equation of the tangent line to the curve f(x) = x² + 5x at x = 3. x→a
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Describe the graph of the function

f(x)=-2sin(x)+3


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