Unit 1 Review

Classify $2(x-3)=2x-6$.

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Factor$$x^2-5x+6$$

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State the excluded input of $\frac{1}{x-7}$.

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Evaluate $f(-2)$ for $f(x)=x^2+3x$.

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Explain why this conclusion is valid: Mark equation solving ready and route only the rational-expression strand to repair. Use the foundation problem as evidence: A learner solves every linear equation but cancels terms illegally in rational expressions.

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Solve$$x^2-7x+12=0$$

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Solve$$|2x-1|=7$$

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Solve$$3^(x+1)=81$$

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Solve$$4-2x\le 10$$

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Explain why this conclusion is valid: The domain requires $x\ge 1$. Squaring gives candidates $0$ and $3$; only $x=3$ checks. Use the foundation problem as evidence: Solve $sqrt(x+1)=x-1$.

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Factor$$8x^2-12x$$

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Factor$$x^2-25$$

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Factor$$x^2+10x+25$$

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List zeros of $(x+1)^2(x-5)$.

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Explain why this conclusion is valid: Let $u=x^2$. Then $(u-1)(u-4),$ so $(x-1)(x+1)(x-2)(x+2)$. Use the foundation problem as evidence: Factor $x^4-5x^2+4$.

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State restrictions of $\frac{5}{x(x-3)}$.

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Simplify$$\frac{x^2-16}{x-4}$$

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Solve$$\frac{1}{x}=\frac{1}{5}$$

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Why can $\frac{x+4}{x}$ not become $4$?

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Explain why this conclusion is valid: The result is $\frac{x+3}{x+2},$ with $x\ne 2,-2$. Use the foundation problem as evidence: Simplify $\frac{x^2+x-6}{x^2-4}$.

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Simplify$$sqrt(48)$$

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Evaluate$$16^(\frac{3}{4})$$

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State domain of $sqrt(3-x)$.

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Simplify$$sqrt(x^2)$$

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Explain why this conclusion is valid: Candidates are $3$ and $-2$; only $x=3$ satisfies the original equation. Use the foundation problem as evidence: Solve $sqrt(x+6)=x$.

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Simplify$$\frac{x^5}{x}^2$$

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Evaluate$$log_5(125)$$

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Expand$$log_b(xy^2)$$

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Solve$$3^x=81$$

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Explain why this conclusion is valid: $-3,$ because $3^(-3)=\frac{1}{27}$. Use the foundation problem as evidence: Evaluate $log_3(\frac{1}{27})$.

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If $f(x)=3x-1,$ find $f(4)$.

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State range with minimum $-2$ and no upper bound.

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Meaning of an open circle at $(3,5)$.

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Graph meaning of$$f(x)=0$$

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Explain why this conclusion is valid: $x=\pm 3$. Use the foundation problem as evidence: If $f(x)=x^2,$ solve $f(x)=9$.

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Factor$$x^3-9x$$

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Average rate of $x^2$ from $1$ to $4$.

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What does a polynomial sign change guarantee?

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One valid use of graphing technology.

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Explain why this conclusion is valid: Domain $[1,4)∪(4,∞)$; zero $x=1$. Use the foundation problem as evidence: Find domain and zero of $\frac{sqrt(x-1)}{x-4}$.

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