Which of the following functions are continuous for all real numbers? h(x)=(1)/(x^(2)) g(x)=x^(2) Choose 1 answer: (A) h only (B) g only (C) Both h and g (D) Neither h nor g

Analyzing h(x) = 1/x^2: Analyze the function h(x) = 1/x^2. Check for points of discontinuity.Discontinuity at x = 0: The function h(x) = 1/x^2 has a denominator that can be zero when x = 0. This means the function is not defined at x = 0 and therefore is not continuous at x = 0.Analyzing g(x) = x^2: Analyze the function g(x) = x^2. Check for points of discontinuity.Continuity of g(x): The function g(x) = x^2 is a polynomial function. Polynomial functions are continuous everywhere on the real number line.Conclusion: Since h(x) is not continuous at x = 0 and g(x) is continuous everywhere, the function that is continuous for all real numbers is g(x) only.

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Which of the following functions are continuous for all real numbers?

h(x)=(1)/(x^(2))

g(x)=x^(2)
Choose 1 answer:
(A)
h only
(B)
g only
(C) Both
h and
g
(D) Neither
h nor
g

Which of the following functions are continuous for all real numbers? $\newline$ $h(x)=\frac{1}{x^{2}}$ $\newline$ $g(x)=x^{2}$ $\newline$ Choose $1$ answer: $\newline$ (A) $h$ only $\newline$ (B) $g$ only $\newline$ (C) Both $h$ and $g$ $\newline$ (D) Neither $h$ nor $g$

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Math Problems

Algebra 1

Domain and range of quadratic functions: equations

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Q. Which of the following functions are continuous for all real numbers?

\newline

h(x)=\frac{1}{x^{2}}

\newline

g(x)=x^{2}

\newline

Choose

1

answer:

\newline

(A)

h

only

\newline

(B)

g

only

\newline

h

and

g

\newline

(D) Neither

h

nor

g

Analyzing $h(x) = \frac{1}{x^2}$ : Analyze the function $h(x) = \frac{1}{x^2}$ . Check for points of discontinuity.
Discontinuity at $x = 0$ : The function $h(x) = \frac{1}{x^2}$ has a denominator that can be zero when $x = 0$ . This means the function is not defined at $x = 0$ and therefore is not continuous at $x = 0$ .
Analyzing $g(x) = x^2$ : Analyze the function $g(x) = x^2$ . Check for points of discontinuity.
Continuity of $g(x)$ : The function $g(x) = x^2$ is a polynomial function. Polynomial functions are continuous everywhere on the real number line.
Conclusion: Since $h(x)$ is not continuous at $x = 0$ and $g(x)$ is continuous everywhere, the function that is continuous for all real numbers is $g(x)$ only.