The graph of a function g is shown.The x y-coordinate plane is given. A function labeled y = g(x) with 4 parts is graphed.The first part is a curve, enters the window in the second quadrant, goes up and right becoming less steep, crosses the y-axis at approximately y = 2.5, and ends at the open point (2, 3).The second part is a curve begins again at the open point (2, 1), goes up and right becoming less steep, and ends at the open point (5, 2).The third part is the closed approximate point (5, 1.2).The fourth part is a curve, begins at the open point (5, 2) goes down and right becoming more steep, and exits the window in the first quadrant.Use it to state the values (if they exist) of the following:(a)  lim x → 2− g(x)(b)  lim x → 2+ g(x)(c)  lim x → 2 g(x)(d)  lim x → 5− g(x)(e)  lim x → 5+ g(x)(f)  lim x → 5 g(x)SolutionLooking at the graph we see that the values of g(x) approach as x approaches 2 from the left, but they approach as x approaches 2 from the right.Therefore (a) lim x → 2− g(x) =     and    (b) lim x → 2+ g(x) = .Since the left and right limits are different, we conclude that (c) the limit as x approaches 2 of g(x) does not exist.The graph also shows that (d) lim x → 5− g(x) =     and    (e) lim x → 5+ g(x) = .This time, the left and right limits are the same and so, by this theorem, we have (f) lim x → 5 g(x) = Despite this fact, notice that g(5) ≠ 2.

The graph of a function g is shown. The x y-coordinate plane is given. The curve begins at the point (−2, 0), goes up and right, passes through the point (−1.5, 1), goes up and right, changes direction at the point (−1, 1.5), goes down and right, passes through the point (−0.5, 1), goes down and right, passes through the origin, goes down and right, passes through the point (0.5, −1), goes down and right, changes direction at the point (1, −1.5), goes up and right, passes through the point (1.5, −0.5), goes up and right, changes direction at the point (2, 0.5), goes down and right, crosses the x-axis at x = 2.5, goes down and right, changes direction at the point (3, −1), goes up and right, passes through the point (3.5, −0.5), goes up and right, and ends at the point (4, 0.5). Estimate 4 −2 g(x) dx with six subintervals using the following. (a) right endpoints 0 Correct: Your answer is correct. (b) left endpoints -0.5 Correct: Your answer is correct. (c) midpoints

The graph of a function f is given in the figure.A curve is shown on the x y coordinate plane. It begins at the point (−2, −1), goes up and to the right, passes through the approximate point (−1, −0.2), and passes through the negative x-axis at the approximate point (−0.8, 0). It then continues up and right, passes through the positive y-axis at the point (0, 1), and reaches a high point at (1, 3). It then goes down and right, passes through the points (2, 2) and (3, 1), and ends at the approximate point (4, 0.5).(a)Find the value of f(1).(b)Estimate the value of f(−1).(c)For what values of x is f(x) = 1? (Enter your answers as a comma-separated list.) (d)Estimate the value of x such that f(x) = 0.x = (e)State the domain and range of f. (Enter your answers in interval notation.)domain range (f)On what interval is f increasing? (Enter your answer using interval notation.)

Graphs of f and g are shown.There are two curves on the x y coordinate plane.A curve labeled f enters the top of second quadrant, goes down and right, crosses the negative x-axis and reaches a minimum in third quadrant, then goes up and right and intersects the origin, and reaches a maximum in first quadrant the same distance away from the x and y axes as its minimum was away from them. It then goes down and right, intersects the positive x-axis the same distance away from the origin as it intersected the negative x-axis, and exits the bottom of fourth quadrant, the same distance away from the x and y axes as was its entry point.A curve labeled g is always above the curve labeled f. g enters the top of second quadrant, goes down and right, reaches a minimum in second quadrant, goes up and right, then reaches a local maximum as it crosses the positive y-axis, and goes down and right. Then it reaches a minimum in first quadrant the same distance away from the x and y axes as was its first minimum. It then goes back up and exits the top of first quadrant the same distance away from the x and y axes as was its entry point.Is f even, odd, or neither?evenodd    neitherExplain your reasoning.It is symmetric about the origin.It is symmetric with respect to the y-axis.    It is symmetric with respect to the x-axis.It is not symmetric about the origin or the y-axis.Is g even, odd, or neither?evenodd    neitherExplain your reasoning.It is symmetric about the origin.It is symmetric with respect to the y-axis.    It is symmetric with respect to the x-axis.It is not symmetric about the origin or the y-axis.

For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)The x y coordinate plane is given. The curve enters the window at the point (−5, 0), goes up and right to the open point (−3, 4), and goes down and right to the closed point (0, 1). The curve starts again at the open point (0, −1), goes up and right to the open point (2, 2), and then oscillates at an increasing rate between y = 2 and y = 4 until it reaches the x-value of 5. Between the x-values of 4.5 and 5 the oscillations are too close together to distinguish individual curves. At (5, 3) the oscillations stop and the curve goes up and right, changes direction at the approximate point (7, 4.8), goes down and right, and exits the window in the second quadrant.(a)lim x → −3− h(x)(b)lim x → −3+ h(x)(c)lim x → −3 h(x)(d)h(−3)(e)lim x → 0− h(x)(f)lim x → 0+ h(x)(g)lim x → 0 h(x)(h)h(0)(i)lim x → 2 h(x)(j)h(2)(k)lim x → 5+ h(x)(l)lim x → 5− h(x)

The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.)The x y-coordinate plane is given. A function with four parts, labeled y = f(x), is shown.The first part is a curve, enters the window in the second quadrant, goes down and right becoming less steep, crosses the x-axis at x = −2, and ends at the point (−1, −1).The second part is linear, starts at the point (−1, −1), goes up and right, passes through the x-axis at x = 0, and ends at the open point (2, 2).The third part is a closed point located at (2, 1).The last part is linear, starts at the open point (2, 2), goes down and right, and exits the window in the first quadrant. The x y-coordinate plane is given. A function with two parts, labeled y = g(x), is shown.The first part is a curve, enters the window in the third quadrant, goes up and right becoming less steep, crosses the x-axis at x = −1, crosses the y-axis at approximately 1.3, and ends at the open point (1, 2).The second part is a curve, begins at the closed point (1, 1), goes down and right becoming more steep, crosses the x-axis at x = 2, and exits the window in the fourth quadrant.(a)lim x→2 [f(x) + g(x)] (b)lim x→1 [f(x) + g(x)] (c)lim x→0 [f(x)g(x)] (d)lim x→−1 f(x)g(x) (e)lim x→2 [x3f(x)] (f)lim x→1 3 + f(x)