Making a Function Continuous In Exercises 63–68, find the constant a , or the constants a and b , such that the function is continuous on the entire real number line. f ( x ) { 2 , x ≤ − 1 a x + b − 1 < x < 3 − 2 x ≥ 3
Making a Function Continuous In Exercises 63–68, find the constant a , or the constants a and b , such that the function is continuous on the entire real number line. f ( x ) { 2 , x ≤ − 1 a x + b − 1 < x < 3 − 2 x ≥ 3
Solution Summary: The author explains that the function is a linear piecewise function and the possible discontinuity is at -1 and 3.
Making a Function Continuous In Exercises 63–68, find the constant a, or the constants a and b, such that the function is continuous on the entire real number line.
f
(
x
)
{
2
,
x
≤
−
1
a
x
+
b
−
1
<
x
<
3
−
2
x
≥
3
Suppose f and g are the piecewise-defined functions defined
here. For each combination of functions in Exercises 51–56,
(a) find its values at x = -1, x = 0, x = 1, x = 2, and x = 3,
(b) sketch its graph, and (c) write the combination as a
piecewise-defined function.
f(x) = {
(2x + 1, ifx 0
g(x) = {
-x, if x 2
8(4):
51. (f+g)(x)
52. 3f(x)
53. (gof)(x)
56. g(3x)
54. f(x) – 1
55. f(x – 1)
In Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function.
f(x)=\frac{6-x}{\sqrt{x}}
In Exercises 83–86, determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.
If the graph of a function has three x-intercepts, then it musthave at least two points at which its tangent line is horizontal
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