Unit 3 Review

$\frac{Domain}{range}$ of $x^2$.

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Parent with sharp corner.

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Quadratic table pattern.

The complete prompt remains readable and printable without JavaScript.

Exponential table pattern.

The complete prompt remains readable and printable without JavaScript.

Explain why this conclusion is valid: Square-root family. Use the foundation problem as evidence: Defined for $x\ge 0,$ starts at the origin, increases while flattening.

The complete prompt remains readable and printable without JavaScript.

Map $(1,4)$ under $f(x)+3$.

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Map under $f(x-2)$.

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Map under -f(x).

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Map under $f(-x)$.

The complete prompt remains readable and printable without JavaScript.

Explain why this conclusion is valid: $(2,3)$. Use the foundation problem as evidence: Map $(8,3)$ under $f(4x)$.

The complete prompt remains readable and printable without JavaScript.

Vertex of $|x|+6$.

The complete prompt remains readable and printable without JavaScript.

Range of $sqrt(x)-2$.

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HA of $5^x+7$.

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Map $(-2,5)$ under $f(x)-8$.

The complete prompt remains readable and printable without JavaScript.

Explain why this conclusion is valid: Vertex $(0,-5),$ range $[-5,∞),$ zeros $\pm sqrt(5)$. Use the foundation problem as evidence: Describe $x^2-5$.

The complete prompt remains readable and printable without JavaScript.

Endpoint of $sqrt(x+5)$.

The complete prompt remains readable and printable without JavaScript.

Vertex of $(x-7)^2$.

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Move $(-2,4]$ right $3$.

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Map $(5,-2)$ under $f(x+3)$.

The complete prompt remains readable and printable without JavaScript.

Explain why this conclusion is valid: Endpoint $(4,0),$ domain $[4,∞)$. Use the foundation problem as evidence: Describe $sqrt(x-4)$.

The complete prompt remains readable and printable without JavaScript.

Reflect $x^2$ across x-axis.

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Reflect sqrt(x) across y-axis.

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Map $(3,-5)$ across x-axis.

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Classify $x^2+x$.

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Explain why this conclusion is valid: Even. Use the foundation problem as evidence: Classify $x^4-3x^2+1$.

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Describe $5|x|$.

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Describe $f(\frac{x}{3})$.

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Map $(8,-1)$ under $f(4x)$.

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Range $[1,4]$ under $-2f$.

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Explain why this conclusion is valid: $(2,-8)$. Use the foundation problem as evidence: Map $(6,4)$ under $-2f(3x)$.

The complete prompt remains readable and printable without JavaScript.

Vertex of $3(x+2)^2-7$.

The complete prompt remains readable and printable without JavaScript.

Endpoint of $-sqrt(x-5)+4$.

The complete prompt remains readable and printable without JavaScript.

Asymptotes of $\frac{2}{x+1}-3$.

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General point map.

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Explain why this conclusion is valid: Vertex $(3,5),$ range $(-∞,5],$ reflected and stretched. Use the foundation problem as evidence: Graph $-2|x-3|+5$.

The complete prompt remains readable and printable without JavaScript.

$f=2x,g=x^2$; $f+g$.

The complete prompt remains readable and printable without JavaScript.

If $f(2)=5,g(2)=-1$.

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Domain $sqrt(x-3)+ln x$.

The complete prompt remains readable and printable without JavaScript.

If $g-f=7,$ f-g.

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Explain why this conclusion is valid: Profit $12q-500$. Use the foundation problem as evidence: Revenue $30q$ and cost $500+18q$.

The complete prompt remains readable and printable without JavaScript.

Zeros of $x(x-5)$.

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Domain $\frac{x+1}{x}^2$.

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If $f(3)=2,g(3)=-4,$ product.

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Quotient.

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Explain why this conclusion is valid: $\frac{f}{g}=x+1$ for $x\ne 1,$ with a hole at $(1,2)$. Use the foundation problem as evidence: $f=x^2-1,g=x-1$.

The complete prompt remains readable and printable without JavaScript.

Vertex $(1,2),$ point $(3,10)$.

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Absolute value vertex $(4,-1),$ point $(6,5)$.

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Root endpoint $(2,-3),$ point $(6,1)$.

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One clue for uniqueness.

The complete prompt remains readable and printable without JavaScript.

Explain why this conclusion is valid: $f(x)=2(x-2)^2-3$. Use the foundation problem as evidence: Parabola vertex $(2,-3),$ point $(4,5)$.

The complete prompt remains readable and printable without JavaScript.