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College Algebra

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Functions And Their Graphs

Section2.6: Combinations Of Functions: Composite Functions

Problem 69E

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Find f0g, g0f and the domain For f(x)= ………, g(x)= x^3+1 Question 36

Finding Domains of Functions and
Composite Functions In Exercises
35-42, find (a) ƒ °g and (b) g•f. Find the
domain of each function and of each composite
function.
35. f(x) = /x + 4, g(x) = x²
36. f(x) 3D Ух
%3|
x – 5, g(x) = x³ + 1
-

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Finding Domains of Functions andComposite Functions In Exercises35–42, find (a) f ∘ g and (b) g ∘ f. Find thedomain of each function and of each compositefunction.35. f(x) = √x + 4, g(x) = x236. f(x) =√3 x − 5, g(x) = x3 + 137. f(x) = x3, g(x) = x2338. f(x) = x5, g(x) = √4 x39. f(x) = ∣x∣, g(x) = x + 640. f(x) = ∣x − 4∣, g(x) = 3 − x41. f(x) = 1x, g(x) = x + 342. f(x) = 3x2 − 1, g(x) = x + 1
Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes. f(x) = 5x/ x2 +25 x-intercept(x, y) = y-intercept(x, y) = relative maximum (x, y) = relative minimum (x, y) = point of inflection (smallest x-value)(x, y) = point of inflection(x, y) = point of inflection (largest x-value)(x, y) = horizontal asymptote= vertical asymptote=
Writing an Equation from a DescriptionIn Exercises 39–46, write an equation for thefunction whose graph is described.39. The shape of f(x) = x2, but shifted three units to theright and seven units down40. The shape of f(x) = x2, but shifted two units to the left,nine units up, and then reflected in the x-axis41. The shape of f(x) = x3, but shifted 13 units to the right42. The shape of f(x) = x3, but shifted six units to the left,six units down, and then reflected in the y-axis43. The shape of f(x) = ∣x∣, but shifted 12 units up andthen reflected in the x-axis44. The shape of f(x) = ∣x∣, but shifted four units to the leftand eight units down45. The shape of f(x) = √x, but shifted six units to the leftand then reflected in both the x-axis and the y-axis46. The shape of f(x) = √x, but shifted nine units downand then reflected in both the x-axis and the y-axis
Finding Values for Which f(x) = g(x)In Exercises 43–46, find the value(s) of x forwhich f(x) = g(x).43. f(x) = x2, g(x) = x + 244. f(x) = x2 + 2x + 1, g(x) = 5x + 1945. f(x) = x4 − 2x2, g(x) = 2x246. f(x) = √x − 4, g(x) = 2 − x
Determining Concavity In Exercises 3–14,determine the open intervals on which the graphof the function is concave upward or concavedownward.' 3. f (x) = x2 − 4x + 8
Activity 2: Let us try to find where a function is increasing or decreasing given the following. 1. f(x) = x3−4x, for x in the interval [−1,2]2. h(x)=−x3 + 3x2 + 93. y = 2x – 5 on interval ( - ∞, ∞)
Analyze and sketch the graph of the function. Identify any intercepts, relative extrema, points of inflection, and asymptotes y = 4x2 − 8x + 2 x-intercept (smaller x-value) (x, y) = x-intercept (larger x-value) (x, y) = y-intercept (x, y) = relative maximum (x, y) = relative minimum (x, y) = point of inflection (x, y) = horizontal asymptote vertical asymptote
Approximating Relative Minima orMaxima In Exercises 49–54, use a graphingutility to approximate (to two decimal places)any relative minima or maxima of the function.49. f(x) = x(x + 3)50. f(x) = −x2 + 3x − 251. h(x) = x3 − 6x2 + 1552. f(x) = x3 − 3x2 − x + 153. h(x) = (x − 1)√x54. g(x) = x√4 − x
A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.
Determining Differentiability. Describe the x-values at which f is differentiable.
Average Rate of Change of a FunctionIn Exercises 61–64, find the average rate ofchange of the function from x1 to x2.Function x-Values61. f(x) = −2x + 15 x1 = 0, x2 = 362. f(x) = x2 − 2x + 8 x1 = 1, x2 = 563. f(x) = x3 − 3x2 − x x1 = −1, x2 = 264. f(x) = −x3 + 6x2 + x x1 = 1, x2 = 6
Testing for Functions RepresentedAlgebraically In Exercises 11–18,determine whether the equation represents yas a function of x.11. x2 + y2 = 4 12. x2 − y = 913. y = √16 − x2 14. y = √x + 515. y = 4 − ∣x∣ 16. ∣y∣ = 4 − x17. y = −75 18. x − 1 = 0

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