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## Solving Radical Equations

/0 Comments/in Accuplacer, Algebra, Math Test Prep /by Jill HackerThis post about solving radical equations is part of a series of posts to help you prepare for the Advanced Algebra and Functions part of the Accuplacer test.## Question

Does the equation have a real solution? If so, what is it?

## Solution

This kind of equation is called a

radical equation, because it contains a radical — in this case, a square root.Let’s try to solve this radical equation:

Subtract 5 from each side:

The square root of something equals something negative? Really? The definition of square root specifies that it means a positive number. But this square root is supposed to equal something negative.

No real solution.You may be tempted to keep going from

and see what happens. OK, let’s try that. Follow the usual steps for solving a radical equation:

There’s a solution: . Now let’s see if it works. Substitute back into the left-hand side of the original equation. You should get:

That simplifies to:

So what looked like the wrong way was indeed the wrong way, the solution does not work, and the answer to the question is

No, the equation does not have a real solution.This question is similar to question number 14 in the sample questions for the Accuplacer Advanced Algebra and Functions test.

## Is This Relation a Function?

/0 Comments/in Accuplacer, Algebra, Math Test Prep /by Jill HackerThis post about whether a relation is a function is part of a series of posts to help you prepare for the Advanced Algebra and Functions part of the Accuplacer test.

## Question

One or more of the graphs below represent 𝑦 as a function of 𝑥. Which one or ones?

A

B

C

D

## Solution

Function/not function?

A function is a relation – that is, a correspondence between

xandy– for which everyx-value relates to only oney-value. No vertical line will pass through more than one point on a function’s graph, but a vertical line may pass through more than one point on the graph of a relation that is not a function. Thus you can use the vertical line test on a relation to see whether it is a function.Look at relation A. Imagine sliding a vertical line across it. At no point will the line intersect the relation more than once. This relation

is a function.Now look at relation B. The

y-axis, which is a vertical line, intersects the relation in three places. Thus relation B fails the vertical line test and relationB is not a function.Relation C: Again, there are places where you could draw a vertical line and cross the relation more than once. For example, the y-axis crosses the relation twice. This relation is

not a function.Relation D: There is only one

x-value where it looks like a vertical line could cross this relation twice: thex-value at the right-hand end of the lower piece, which is thex-value at left-hand end of the upper piece. Are there twoy-values at thisx-value? The lower piece, in which the circle is filled in, does take thisx-value. But the upper piece, in which the circle is not filled in, does not take the value. Thus there is nox-value that both pieces take, and there is nox-value for which there is more than one value ofThis relation is a function.𝑨𝒏𝒔𝒘𝒆𝒓:

A and DThis question is similar to #6 in the sample questions for the Accuplacer Advanced Algebra and Functions test.