3. Functions

Intro to Functions & Their Graphs

3. Functions

Intro to Functions & Their Graphs

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Multiple Choice

Is the equation $y^2+2x=10$ a function? If so, rewrite it in function notation and evaluate at $f\left(-1\right)$ .

$f\left(-1\right)=\sqrt{12}$ , Is A Function

$f\left(-1\right)=12$ , Is A Function

$f\left(-1\right)=\frac92$ , Is A Function

Is NOT A Function

Verified step by step guidance

Step 1: Begin by examining the given equation y^2 + 2x = 10. To determine if this is a function, recall that a function must have only one output (y-value) for each input (x-value).

Step 2: Consider the equation y^2 + 2x = 10. Rearrange it to isolate y^2: y^2 = 10 - 2x.

Step 3: Notice that y^2 = 10 - 2x implies y = ±√(10 - 2x). This indicates that for each x-value, there are potentially two y-values (one positive and one negative), which violates the definition of a function.

Step 4: Since the equation y^2 + 2x = 10 can produce more than one y-value for a given x-value, it is not a function.

Step 5: Therefore, the equation y^2 + 2x = 10 is not a function, and it cannot be rewritten in function notation or evaluated at f(-1).

5:2m

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Intro to Functions & Their Graphs practice set

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Go to Practice

Struggling with College Algebra?

Is the equation y2+2x=10y^2+2x=10y2+2x=10 a function? If so, rewrite it in function notation and evaluate at f(−1)f\left(-1\right)f(−1).

Watch next

Intro to Functions & Their Graphs practice set

Is the equation $y^2+2x=10$ a function? If so, rewrite it in function notation and evaluate at $f\left(-1\right)$ .