Let fand g be the functions whose graphs are shown below. 3 2 - -4 2...
2. The graphs of functions f and g are shown below. Circle your choice for each of the questions below. 1 3 2 g 0 2 a. Let u(x) = 160. Find the value of '(1) g(x) ii. 3 9 iv. / V. None of the above b. Let v(x) = x2. [f(x)]'. Find the value of v'(6). i. 1296 ii. -81 iii. 567 iv. 81 V. None of the above
Let H(X)=f(x) + 5g(x), where the graphs of fand g are shown in the figure to the right. Find H'(4). 10- 8- 6- 44 2- ok 0 4 6 8 10 H (4)-( ch ht! nti
O GRAPHS AND FUNCTIONS Sum, difference, and product of two functions Suppose that the functions,fand g are defined for all real numbers r as follows. 2 g) 2 and evaluate (g n-. Write the expressions for (g-f)(x) and (g+f(r) and evaluate (g.)(-1). (e11)-D
O GRAPHS AND FUNCTIONS Composition of a function with itself Suppose that the functions fand g are defined as follows. f(x)--, x#0 g(x)-x2-9 Find the compositions f fand g'g. Simplify. your answers as much as possible. Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the doma Explanation Check
3) Determine the values below using the graphs of fand g shown. If a value is not defined, state "not defined." Assume the ends of fand g continue the shape you see beyond the graph. Ax) c) 2-5(g(0)-3) (Read carefully.) d) 9(3) a e) g-2) 6-2 9) R-3)+9(5) h) For what values of x does g(x)-2? i) For what values of x is fdecreasing? D For what values of x is g increasing? k) Give three values that g(x) can...
5 Consider the functions f and g whose graphs are given below. z y = f(x) -4 A3 -2 -1 1 2 3 4 y = 9(2) -4 -3 -2 -1 1 2 3 4 1 + f. Find (3) a. Find f'(-3). b. Find f'(1). g. Suppose p(x) = f(x)g(2). Find p'(-3). c. Find f'(3). h. Suppose q(z) = 5(). Find g(3). d. Find t'(-3). g(2) e. Find g'(1). i. Suppose r(x) = x2 f(x). Find r'(1).
3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and w(x)-g(f(x)) Use the graphs to find the indicated derivatives. If the indicated derivative does not exist, write "D.N.E." in the space provided. Be sure to include work that shows how you arrived at your answer. 20 a) u'3) b) v-4) c) wl) 3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and...
Question 7 7. For each pair of functions fand g below, find (x)) and g (fx). Then, determine whether fand g are inverses of each other Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) (x) 2x x1 (b) f(x) =T g (x)=2x + 1 f(g (x)) = f(g (x)) = fand g are inverses of each other...
5. Given below are the graphs of two functions (x) and g(x) both functions are defined on[0,5].Let h(x)-(g(x)). Use the graphs to determine the sevalues of the critical points ofh(x).Explain Credit will not be given if no explanation is provided) f(x) g(x) 4 4 Esplanation/work used to determine the values of the critical points of h(x) The -values of the critical points of h(x) are 5. Given below are the graphs of two functions (x) and g(x) both functions are...
Problem 3 Given the following graphs of f and g (both piecewise linear functions), define new functions u(r) = f(g(x)) and v() = f(g(). Find: 9 0 1 (a) (1) (b) v' (1)