 1.1.1: Express the area and circumference of a circle as functions of the ...
 1.1.2: Express the radius of a sphere as a function of the sphere's surfac...
 1.1.3: A point P in the frrst quadrant lies on the parabola y = x 2 Expres...
 1.1.4: A hotair balloon rising straight up from a level field is traclred...
 1.1.5: Iu Exercises 51!, determine whether the graph of the function is ...
 1.1.6: Iu Exercises 51!, determine whether the graph of the function is ...
 1.1.7: Iu Exercises 51!, determine whether the graph of the function is ...
 1.1.8: Iu Exercises 51!, determine whether the graph of the function is ...
 1.1.9: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.10: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.11: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.12: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.13: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.14: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.15: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.16: InExercises 916, deterntine v.lrether the function is even, odd, o...
 1.1.17: Suppose that f and g are both odd functions defined on the entire r...
 1.1.18: If f(a  x) = f(a + x), show that g(x) = f(x + a) is an even function.
 1.1.19: In Exercises 19~28, fmd the (a) domain and (b) range. y = Ixl  2
 1.1.20: In Exercises 19~28, fmd the (a) domain and (b) range. y = 2 + ~
 1.1.21: In Exercises 19~28, fmd the (a) domain and (b) range. y = Vl6  x2
 1.1.22: In Exercises 19~28, fmd the (a) domain and (b) range. y = 32> + I
 1.1.23: In Exercises 19~28, fmd the (a) domain and (b) range. y = 2e~  3
 1.1.24: In Exercises 19~28, fmd the (a) domain and (b) range. y = tsn(2x  ...
 1.1.25: In Exercises 19~28, fmd the (a) domain and (b) range. y = 2sin(3x +...
 1.1.26: In Exercises 19~28, fmd the (a) domain and (b) range. y = x 2/'
 1.1.27: In Exercises 19~28, fmd the (a) domain and (b) range. y = Iu (x  3...
 1.1.28: In Exercises 19~28, fmd the (a) domain and (b) range. y = I + ~2  x
 1.1.29: State whether each function is increasing, decreasing, or neither. ...
 1.1.30: Find the largest interval on which the given function is increasing...
 1.1.31: In Exercises 31 and 32, fmd the (a) domain and (b) range. y Yx, 0<xs4
 1.1.32: In Exercises 31 and 32, fmd the (a) domain and (b) range. y= x, 'x...
 1.1.33: In Exercises 33 and 34, write a piecewise formula for the function.
 1.1.34: In Exercises 33 and 34, write a piecewise formula for the function.
 1.1.35: In Exercises 35 and 36, rmd x+2I 35. f
 1.1.36: In Exercises 35 and 36, rmd f(x) = 2  x, g(x) = V'x+l
 1.1.37: In Exercises 37 and 38, f(x) = 2  x 2, g(x) = Vx+2
 1.1.38: In Exercises 37 and 38, f(x) = Yx, g(x) = ~
 1.1.39: For Exercises 39 and 40, sketch the graphs of f and f " f. f(x) = {...
 1.1.40: For Exercises 39 and 40, sketch the graphs of f and f " f. f x = x ...
 1.1.41: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.42: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.43: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.44: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.45: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.46: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.47: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.48: In Exercises 4148, graph h and h together. Then describe how apply...
 1.1.49: Suppose the graph of g is given. Write equations for the graphs tha...
 1.1.50: Describe how each graph is obtained from the graph ofy = f(x). a. y...
 1.1.51: In Exercises 5154, graph each function, not by plotting points, bu...
 1.1.52: In Exercises 5154, graph each function, not by plotting points, bu...
 1.1.53: In Exercises 5154, graph each function, not by plotting points, bu...
 1.1.54: In Exercises 5154, graph each function, not by plotting points, bu...
 1.1.55: In Exercises 5558, sketch the graph of the given function. What is...
 1.1.56: In Exercises 5558, sketch the graph of the given function. What is...
 1.1.57: In Exercises 5558, sketch the graph of the given function. What is...
 1.1.58: In Exercises 5558, sketch the graph of the given function. What is...
 1.1.59: Sketch the graph y = 2 cos (x f) Sketch the graph y = 2 cos (x f).
 1.1.60: Sketch the graph y = 1 + sin (x + .;(J Sketch the graph y = 1 + sin...
 1.1.61: In Exercises 6164, ABC is a right triangle with the right angle at...
 1.1.62: In Exercises 6164, ABC is a right triangle with the right angle at...
 1.1.63: In Exercises 6164, ABC is a right triangle with the right angle at...
 1.1.64: In Exercises 6164, ABC is a right triangle with the right angle at...
 1.1.65: Two wires s1retch from the top T of a vertical pole to points B and...
 1.1.66: Observers at positions A and B 2 kIn apart simultaneously measure t...
 1.1.67: a. Graphthefunctionf(x) = sinx + cos(x/2). b. What appears to be th...
 1.1.68: a. Graphf(x) = sin (llx). b. What are the domain and range off? c. ...
Solutions for Chapter 1: Functions
Full solutions for Thomas' Calculus  12th Edition
ISBN: 9780321587992
Solutions for Chapter 1: Functions
Get Full SolutionsSince 68 problems in chapter 1: Functions have been answered, more than 9923 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Thomas' Calculus was written by and is associated to the ISBN: 9780321587992. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1: Functions includes 68 full stepbystep solutions.

Addition property of equality
If u = v and w = z , then u + w = v + z

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Complex conjugates
Complex numbers a + bi and a  bi

Convenience sample
A sample that sacrifices randomness for convenience

DMS measure
The measure of an angle in degrees, minutes, and seconds

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Logarithm
An expression of the form logb x (see Logarithmic function)

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Regression model
An equation found by regression and which can be used to predict unknown values.

Relevant domain
The portion of the domain applicable to the situation being modeled.

Slopeintercept form (of a line)
y = mx + b

Union of two sets A and B
The set of all elements that belong to A or B or both.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.