 1.1.1: If f sxd x 1 s2 2 x and tsud u 1 s2 2 u , is it true that f t?
 1.1.2: If fsxd x 2 2 x x 2 1 and tsxd x is it true that f t?
 1.1.3: The graph of a function f is given. (a) State the value of fs1d. (b...
 1.1.4: The graphs of f and t are given. (a) State the values of fs24d and ...
 1.1.5: Determine whether the curve is the graph of a function of x. If it ...
 1.1.6: Determine whether the curve is the graph of a function of x. If it ...
 1.1.7: Determine whether the curve is the graph of a function of x. If it ...
 1.1.8: Determine whether the curve is the graph of a function of x. If it ...
 1.1.9: Shown is a graph of the global average temperature T during the 20t...
 1.1.10: Trees grow faster and form wider rings in warm years and grow more ...
 1.1.11: A healthy esophagus has a pH of about 7.0. When acid reflux occurs,...
 1.1.12: Tadpole weights The figure shows the average body weights of tadpol...
 1.1.13: Species richness Tropical regions receive more rainfall and intense...
 1.1.14: In this section we discussed examples of ordinary, everyday functio...
 1.1.15: The graph shown gives the weight of a certain person as a function ...
 1.1.16: The graph shows the horizontal force exerted by the ground on a per...
 1.1.17: You put some ice cubes in a glass, fill the glass with cold water, ...
 1.1.18: Three runners compete in a 100meter race. The graph depicts the di...
 1.1.19: Shown is a typical graph of the number N of bacteria grown in a bat...
 1.1.20: Sketch a rough graph of the number of hours of daylight as a functi...
 1.1.21: Sketch a rough graph of the outdoor temperature as a function of ti...
 1.1.22: You place a frozen pie in an oven and bake it for an hour. Then you...
 1.1.23: Sketch the graph of the amount of a particular brand of coffee sold...
 1.1.24: Sketch a rough graph of the market value of a new car as a function...
 1.1.25: Bird count The table shows the number of house finches, in thousand...
 1.1.26: Researchers measured the blood alcohol concentration (BAC) of eight...
 1.1.27: If f sxd 3x 2 2 x 1 2, find fs2d, fs22d, fsad, fs2ad, fsa 1 1d, 2fs...
 1.1.28: A spherical balloon with radius r inches has volume Vsrd 4 3r 3 . F...
 1.1.29: 2932 Evaluate the difference quotient for the given function. Simpl...
 1.1.30: 2932 Evaluate the difference quotient for the given function. Simpl...
 1.1.31: 2932 Evaluate the difference quotient for the given function. Simpl...
 1.1.32: 2932 Evaluate the difference quotient for the given function. Simpl...
 1.1.33: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.34: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.35: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.36: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.37: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.38: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.39: 3339 Find the domain of the function. 33. fsxd x 1 4 x 2 2 9 34. fs...
 1.1.40: Find the domain and range and sketch the graph of the function hsxd...
 1.1.41: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.42: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.43: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.44: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.45: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.46: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.47: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.48: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.49: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.50: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.51: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.52: 4152 Find the domain and sketch the graph of the function. 41. fsxd...
 1.1.53: 5357 Find a formula for the described function and state its domain...
 1.1.54: 5357 Find a formula for the described function and state its domain...
 1.1.55: 5357 Find a formula for the described function and state its domain...
 1.1.56: 5357 Find a formula for the described function and state its domain...
 1.1.57: 5357 Find a formula for the described function and state its domain...
 1.1.58: A cell phone plan has a basic charge of $35 a month. The plan inclu...
 1.1.59: A hotel chain charges $75 each night for the first two nights and $...
 1.1.60: The function in Example 11 is called a step function because its gr...
 1.1.61: Temperature chart The figure shows the temperature of a patient inf...
 1.1.62: A temperature chart is shown for a patient with a fever induced by ...
 1.1.63: Graphs of f and t are shown. Decide whether each function is even, ...
 1.1.64: Graphs of f and t are shown. Decide whether each function is even, ...
 1.1.65: a) If the point s5, 3d is on the graph of an even function, what ot...
 1.1.66: A function f has domain f25, 5g and a portion of its graph is shown...
 1.1.67: 6772 Determine whether f is even, odd, or neither. If you have a gr...
 1.1.68: 6772 Determine whether f is even, odd, or neither. If you have a gr...
 1.1.69: 6772 Determine whether f is even, odd, or neither. If you have a gr...
 1.1.70: 6772 Determine whether f is even, odd, or neither. If you have a gr...
 1.1.71: 6772 Determine whether f is even, odd, or neither. If you have a gr...
 1.1.72: 6772 Determine whether f is even, odd, or neither. If you have a gr...
 1.1.73: If f and t are both even functions, is f 1 t even? If f and t are b...
 1.1.74: If f and t are both even functions, is the product ft even? If f an...
Solutions for Chapter 1.1: Four Ways to Represent a Function
Full solutions for Biocalculus: Calculus for Life Sciences  1st Edition
ISBN: 9781133109631
Solutions for Chapter 1.1: Four Ways to Represent a Function
Get Full SolutionsChapter 1.1: Four Ways to Represent a Function includes 74 full stepbystep solutions. Biocalculus: Calculus for Life Sciences was written by and is associated to the ISBN: 9781133109631. Since 74 problems in chapter 1.1: Four Ways to Represent a Function have been answered, more than 25231 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Biocalculus: Calculus for Life Sciences , edition: 1.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).