effect function become points of new graph f(x) + d (a, b) 7 (a, b + d) shift up by d f(x) d (a, b) 7 The graph of 2g(3x) is obtained from the graph of g(x) by shrinking the horizontal
text gt
x = − + + Let R and S be the two regions enclosed by the graphs of f and g shown in the figure 2 0 0 997427 1 006919 2
ap calculus ab q
e the shaded region bounded by the graph of y = In x and the line y = x - 2, as shown above (a) Find the area Let f and g be the functions given by f(x) = et and g(x) = ln x een r
Calc Sem Unit PT
graph of f (x) intersects both axes 4) If f (x) = 4 x 1 and g(x) = 2x, then the solution set of f (g(x))
AP Calculus Exam Prep Assign KEY
the graph of y = f(x) to graph the function g(x) = f(x + 3) y = f(x) shift 3 units left oa Eco 1 LEHET
. HW
a picture of the graph of g(x) = x2 1 It is obtained from the graph of f(x) = x 2 by shifting it down 1
functions and transformations
h diagram represents a one-to-one function? ID : { x1 x 5 R 0x2 4 / 3 5) The functions f and g are defined by f(x) = x² and g(x) = 2x respectively Find h(x) if h(x) = f(2x)g(–2x)
chapt and ANS
gram above shows the graph of the function f , defined as ( ) 1 4, , 2 1 f x x x Question 19 (***) The functions f and g
function exam questions
Only after f has done its job do you add d to get the new function f(x) + d. 67. ') g. Page 2. Because
function f (x) = x. 2 . Step 2: Now that we know the library function we will be using we need a set of points from the graph of f (x) = x. 2 to work with.
e ? ? ? ? ? ?. ?. = ?. = The slope of the line tangent to the graph of f at. 3. 2 x e ?. ?. 2?. 2 e ?. The absolute minimum value of f on 0. 2 x.
(E) x = 2 is a vertical asymptote of the graph of f. The graph of a differentiable function f is shown above. ... 1(oJ: I ~ (01) ~ (I/O) ~ 5(1)=0. 7.
Suppose we wanted to graph the function defined by the formula g(x) = f(x)+2. Let's take a minute to remind ourselves of what g is doing. We start with an input
A) Find the maximum area of a rectangle that has two vertices on the x-axis and two vertices on the graph of f. Justify your answer. A = lw = 2x. ( )e x2. dA dx.
Sketch the graph of f(x)=3x ? x2 and find If y = x2 + 2x and x = (z ? 2)2 find y when z = 3. b. Given L(x)=2x + 1 and M(x) = x2 ? x
Write a rule for g described by the transformations of the graph of f. 7. f(x) = x²; vertical stretch by a factor of 2 and a reflection in the x-axis followed
7. 6. I. 5. I. A. I. 3. I l J. . J. -1 I. . -s-4 -3 -2 Ao 1 2 3 4 5 6 t 11_2. ._ I. -3. I. I. X. Graph of g. 3. The graph of the continuous function g
Unauthorized copying or reuse of any part of this page is illegal. 2. If ƒ (x) = x³ ? x² + x ? 1 then ƒ'(2) = (A) 10. (B) 9. (C) 7 f'= 3x²-21.
Graph Transformations