Precalculus Final Assessment

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

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

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Simplify$$sqrt(48)$$

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

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Write cost for $\$9$ plus $\$2$ per movie.

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Solve the representation example, then name the feature of function notation, evaluation, and solving that it illustrates: For $g(x)=x^2+1,$ find $g(-3)$.

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Physical domain of side length $s$.

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Solve the representation example, then name the feature of piecewise-defined functions that it illustrates: Meaning of overlapping intervals.

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

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Solve the representation example, then name the feature of vertical translations that it illustrates: Range of$$sqrt(x)-2$$

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Describe $5|x|$.

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Solve the representation example, then name the feature of sums and differences of functions that it illustrates: If$$f(2)=5,g(2)=-1$$

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$f=x+10,g=2x$; $f(g(3))$.

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Undefined versus unknown.

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Solve the representation example, then name the feature of one-to-one functions that it illustrates: Is $x^3$ one-to-one?

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Connect two representations for this example: Verify $f=3x-2$ and $g=\frac{x+2}{3}$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Parity of $x^6$.

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Intercept for zero $-3$.

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Solve the representation example, then name the feature of turning points and local versus global behavior that it illustrates: Max turns degree$$7$$

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Connect two representations for this example: Is $x+2$ a factor of $x^3-3x+2$? Describe what a graph, table, mapping, or algebraic form would have to show.

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Domain of $\frac{1}{x+5}$.

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Connect two representations for this example: Analyze $\frac{1}{x-2}$ near $2$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Solve the representation example, then name the feature of intercepts and sign charts that it illustrates: Y-intercept.

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Which endpoints may be included?

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Classify $3,8,13,18$.

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$50$ doubles every $8$ days.

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Solve the representation example, then name the feature of exponential regression and residuals that it illustrates: Interpret$$b=0.81$$

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Connect two representations for this example: Analyze $log_3(4-2x)$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Solve$$y=x+4 \qquad y=3x-2$$

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Solve the representation example, then name the feature of systems of inequalities and feasible regions that it illustrates: Line style$$y>2x+1$$

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Matrix for $x+y=2,x-y=4$.

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Solve the representation example, then name the feature of gauss-jordan elimination and reduced row-echelon form that it illustrates: Define rank.

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Give one positive and one negative angle coterminal with $310$ degrees.

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Verify “Both subtend $3$ radians.” using the required condition for radian measure as normalized arc length.

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Which unit-circle point corresponds to $t=-\frac{pi}{3}$?

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Verify “$sin(\frac{pi}{3})=\frac{sqrt(3)}{2,} cos(\frac{pi}{3})=\frac{1}{2,} tan(\frac{pi}{3})=sqrt(3)$.” using the required condition for exact values from special triangles.

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State the coordinates of the maximum and minimum of sin $t$ on $[0,2pi]$.

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Find the period and frequency of$$y=cos(\frac{pi t}{6})$$

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Find the period and vertical asymptotes of$$tan(2x)$$

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Evaluate $arctan(-1)$ in its principal range.

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Why does an identity proof need a common domain?

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Find sin $15$ degrees exactly.

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Rewrite sin $8x-sin 2x$ as a product.

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Solve $cos(2x)=0$ on $[0,2pi)$.

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A right triangle has legs $5$ and $12$. Find all six trig ratios for the angle opposite side $5$.

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Verify “$C=67$ degrees; $b=\frac{18sin71}{sin}42$; $c=\frac{18sin67}{sin}42$.” using the required condition for the law of sines.

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A triangle has area $30,$ sides $8$ and $10$ enclosing angle C. Find possible C values.

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Verify “$<80cos135,80sin135>=<-40sqrt(2),40sqrt(2)>$ N.” using the required condition for vectors geometrically and in components.

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Write the circle centered at $(4,-1)$ through $(1,3)$.

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Verify “$a=5,c=4,b=3$; $\frac{x^2}{25}+\frac{y^2}{9}=1$.” using the required condition for ellipses.

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What conic type is suggested by opposite-sign squared terms?

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Verify “It is an ellipse; set distance to focus equal to one-half distance to directrix and simplify.” using the required condition for eccentricity and unified conic structure.

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What changes when $t$ is replaced by -t?

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Can two particles' paths intersect without the particles colliding?

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Where does $r=3cos$ theta pass through the pole?

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Write $4-4i$ in polar form.

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State the domain of $a_n=2n+1$ for $n=0,1,2,$...

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Find $a_8$ for $5,-10,20,$...

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Find$$1+2+...+100$$

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What does the inductive hypothesis allow you to assume?

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Which feature most strongly separates polynomial from exponential end behavior?

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Simplify the difference quotient for$$f(x)=3x+5$$

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Can a limit exist when the function is undefined at the point?

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Why should exact values be retained until late in a calculation?

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