Question

3. Consider $f(x) = \frac{x^2 - 4}{x^2}$, (a) (2 points) Show that this is an even function. (b) (2 points) Rewrite $f(x)$ using factoring, then find its domain. (c) (2 points) Find all its intercepts. (d) (2 points) Find all its asymptotes. (e) (3 points) Graph $f(x)$. (f) (2 points) Find intervals where $f(x) \le 0$.

          3. Consider $f(x) = \frac{x^2 - 4}{x^2}$,
(a) (2 points) Show that this is an even function.
(b) (2 points) Rewrite $f(x)$ using factoring, then find its domain.
(c) (2 points) Find all its intercepts.
(d) (2 points) Find all its asymptotes.
(e) (3 points) Graph $f(x)$.
(f) (2 points) Find intervals where $f(x) \le 0$.

3. Consider f(x) = (x^2 - 4)/(x^2),
(a) (2 points) Show that this is an even function.
(b) (2 points) Rewrite f(x) using factoring, then find its domain.
(c) (2 points) Find all its intercepts.
(d) (2 points) Find all its asymptotes.
(e) (3 points) Graph f(x).
(f) (2 points) Find intervals where f(x) ≤ 0.

Added by Megan D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Allison Knapp

11/08/2022

Step 1

To show that f(x) is an even function, we need to prove that f(-x) = f(x) for all x in the domain of f. f(-x) = ((-x)^2 - 4)/((-x)^2) = (x^2 - 4)/(x^2) = f(x) Since f(-x) = f(x) for all x in the domain, f(x) is an even function. Show more…

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Consider f(x)=(x^(2)-4)/(x^(2)), (a) (2 points) Show that this is an even function. (b) (2 points) Rewrite f(x) using factoring, then find its domain. (c) (2 points) Find all its intercepts. (d) (2 points) Find all its asymptotes. (e) (3 points) Graph f(x). (f) (2 points) Find intervals where f(x) > 0. Total Points: 50 Study Guide 16 Page 3 of 4