0. Review of College Algebra

Functions

0. Review of College Algebra

Functions

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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: Start by analyzing the given equation y^2 + 2x = 10. To determine if it is a function, we need to check if for every x-value there is only one corresponding y-value.

Step 2: Rearrange the equation to express y in terms of x. This involves isolating y on one side of the equation. However, notice that y is squared, which suggests that for some x-values, there might be two possible y-values (one positive and one negative).

Step 3: Consider the definition of a function: a relation where each input (x-value) has exactly one output (y-value). If solving for y results in more than one value for a single x, then the equation is not a function.

Step 4: Attempt to solve for y by isolating y^2: y^2 = 10 - 2x. Taking the square root of both sides gives y = ±√(10 - 2x). The presence of the '±' indicates two possible y-values for each x, confirming it is not a function.

Step 5: Since the equation does not satisfy the definition of a function, it cannot be rewritten in function notation, and evaluating it at f(-1) is not applicable. Therefore, the equation is not a function.