Ch. 1 - Functions

Briggs - Calculus: Early Transcendentals 3rd Edition

Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경

Briggs 3rd Edition

Ch. 1 - Functions

문제 1.21

1장, 문제 1.21

State whether the functions represented by graphs A , B , C and in the figure are even, odd, or neither. <IMAGE>

검증된 단계별 안내

Step 1: Understand the definitions of even and odd functions. An even function satisfies f(x) = f(-x) for all x in its domain, meaning it is symmetric with respect to the y-axis. An odd function satisfies f(-x) = -f(x) for all x in its domain, meaning it is symmetric with respect to the origin.

Step 2: Analyze the symmetry of each graph. For graph A, check if the graph is symmetric with respect to the y-axis (even) or the origin (odd).

Step 3: Repeat the symmetry analysis for graph B. Determine if graph B is symmetric with respect to the y-axis or the origin.

Step 4: Perform the same symmetry check for graph C. Look for y-axis symmetry or origin symmetry to classify the function.

Step 5: Based on the symmetry analysis, classify each function as even, odd, or neither. If a graph does not exhibit symmetry with respect to the y-axis or the origin, it is neither even nor odd.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Even Functions

A function is considered even if its graph is symmetric with respect to the y-axis. Mathematically, this means that for every x in the domain, f(-x) = f(x). Common examples include f(x) = x² and f(x) = cos(x). Identifying even functions involves checking this symmetry visually or through algebraic verification.

Odd Functions

A function is classified as odd if its graph is symmetric with respect to the origin. This means that for every x in the domain, f(-x) = -f(x). Examples include f(x) = x³ and f(x) = sin(x). To determine if a function is odd, one can look for this rotational symmetry or apply the algebraic condition.

Neither Even Nor Odd Functions

A function is neither even nor odd if it does not exhibit the symmetry properties of either category. This can occur when the function has terms that do not conform to the even or odd definitions, such as f(x) = x² + x. To classify a function as neither, one must show that it fails both symmetry tests.

관련 실천

교과서 질문

Solving equations Solve each equation.

√2 sin 3Θ + 1 = 2, 0 ≤ Θ ≤ π

353

views

교과서 질문

Find the inverse $f^{-1}$\left$(x$\right$)$ of each function (on the given interval, if specified).

$f$\left$(x$\right$)=10^{-2x}$

237

views

교과서 질문

Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.

$the log base 6 of 60$

340

views

교과서 질문

Find the inverse $f^{-1}$\left$(x$\right$)$ of each function (on the given interval, if specified).

$f$\left$(x$\right$)=$\frac{2}{x^2+1}$$ , for $x$\geq{0}$$

417

views

교과서 질문

Solving equations Solve the following equations.

ln x= -1

334

views

교과서 질문

The National Weather Service releases approximately $70,000$ radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about $1000$ ft/min until the balloon bursts in the upper atmosphere. Suppose a radiosonde is released from a point $6$ ft above the ground and that $5$ seconds later, it is $83$ ft above the ground. Let $f$\left$(t$\right$)$ represent the height (in feet) that the radiosonde is above the ground $t$ seconds after it is released. Evaluate $\frac{f\left(5\right)-f\left(0\right)}{5-0}$ and interpret the meaning of this quotient.

514

views