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The function
f is defined as
f(x)=x^(2)-1.
What is the
x-coordinate of the point on the function's graph that is closest to the origin?
Choose all answers that apply:
A
-(sqrt3)/(3)
B
-(sqrt2)/(2)
c. 0
D
(sqrt3)/(3)
E
(sqrt2)/(2)

The function $f$ is defined as $f(x)=x^{2}-1$ . $\newline$ What is the $x$ -coordinate of the point on the function's graph that is closest to the origin? $\newline$ Choose all answers that apply: $\newline$ A $-\frac{\sqrt{3}}{3}$ $\newline$ B $-\frac{\sqrt{2}}{2}$ $\newline$ c. $0$ $\newline$ D $\frac{\sqrt{3}}{3}$ $\newline$ E $\frac{\sqrt{2}}{2}$

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Find the vertex of the transformed function

Full solution

Q. The function

f

is defined as

f(x)=x^{2}-1

.

\newline

What is the

x

-coordinate of the point on the function's graph that is closest to the origin?

\newline

Choose all answers that apply:

\newline

A

-\frac{\sqrt{3}}{3}

\newline

B

-\frac{\sqrt{2}}{2}

\newline

c.

0

\newline

D

\frac{\sqrt{3}}{3}

\newline

E

\frac{\sqrt{2}}{2}

Parabola Description: The function $f(x) = x^2 - 1$ is a parabola that opens upwards with its vertex at the origin of the coordinate system.
Vertex Definition: The vertex of the parabola is the point on the graph that is closest to the origin.
Vertex Coordinates: The vertex of the parabola given by $f(x) = x^2 - 1$ is at $(0, -1)$ .
X-coordinate of Vertex: The $x$ -coordinate of the vertex is $0$ , which is the value we are looking for.

More problems from Find the vertex of the transformed function

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h

is defined over the real numbers. This table gives a few values of

h

\newline

\begin{tabular}{lllll}

\newline

x

-6

1

-6

01

-6

001

-5

9

\newline

h(x)

-0

25

-0

74

-0

98

-1

0

\newline

\newline

What is a reasonable estimate for

\lim _{x \rightarrow-6} h(x)

\newline

1

\newline

-6

\newline

-2

\newline

-1

\newline

(D) The limit doesn't exist

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