Explanation Given: The given function is f ( x ) = − 2 5 x + 4 . Concept: a) The leading term is the first term of a polynomial arranged in descending order of their powers. b) The leading coefficient is the coefficient of leading term. c) The degree is the highest power of a polynomial. d) The leading term behaviour of a given curve for a polynomial of degree n can be explained in the following ways, 1. If n is an even number and a n > 0 , then end behaviour of polynomial is given by the curve in figure (1). Figure (1) 2. If n is an even number and a n < 0 , then end behaviour of polynomial is given by the curve in figure (2). Figure (2) 3. If n is an odd number and a n > 0 , then end behaviour of polynomial is given by the curve in figure (3). Figure (3) 4. If n is an odd number and a n < 0 , then end behaviour of polynomial is given by the curve in figure (4). Figure (4) e) The y -intercepts of a function is the point at which graph of the function intersects the y -axis or the value of the function f ( x ) for x = 0

5th Edition

ISBN: 9780321969576

Author: Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Publisher: PEARSON

See similar textbooks

Question

Chapter 4.2, Problem 4VG

To determine

To select:

The appropriate sketch for the given function f(x)=−25x+4 using the knowledge of leading-term test and y-intercepts.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.2, Problem 3VG

Chapter 4.2, Problem 5VG

Students have asked these similar questions

1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.

5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}

For the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)

Chapter 4 Solutions

College Algebra (5th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

Knowledge Booster

To select: The appropriate sketch for the given function f ( x ) = − 2 5 x + 4 using the knowledge of leading-term test and y -intercepts.

To select: The appropriate sketch for the given function f(x)=−25x+4 using the knowledge of leading-term test and y-intercepts.

Want to see the full answer?

Chapter 4 Solutions

To select:

The appropriate sketch for the given function f(x)=−25x+4 using the knowledge of leading-term test and y-intercepts.