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1.1: Academic Success Skills

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.01%3A_Academic_Success_Skills

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3.5: Finding Information About Functions From Graphs

https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/03%3A_Inequalities_and_Functions/3.05%3A_Finding_Information_About_Functions_From_Graphs

Keep in mind that if the graph continues beyond the portion of the graph we can see (as noted by arrows on the ends of the graph), the domain and range may be greater than the visible values shown in ...Keep in mind that if the graph continues beyond the portion of the graph we can see (as noted by arrows on the ends of the graph), the domain and range may be greater than the visible values shown in the coordinate system. The graph may continue to the left and right beyond what is viewed, but based on the portion of the graph that is visible, we can determine the domain as

$1973≤t≤2008$ and the range as approximately

$180≤b≤2010$ .

1.2.9: Factoring ax² + bx + c when a =1

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.09%3A_Factoring_ax__bx__c_when_a_1

Use the left- and right-arrow keys to move the cursor to the left of the first

$x$ -intercept, then press ENTER to mark the “Left bound.” Next, move the cursor to the right of the first

$x$ -interce...Use the left- and right-arrow keys to move the cursor to the left of the first

$x$ -intercept, then press ENTER to mark the “Left bound.” Next, move the cursor to the right of the first

$x$ -intercept, then press ENTER to mark the “Right bound.” Press ENTER to accept the current position of the cursor as your “Guess.” The result is shown in the image on the left in Figure

$\PageIndex{7}$ .

1.2.11: Factoring Special Products

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.11%3A_Factoring_Special_Products

\(\begin{array} {llll} \textbf{Step 1.} &\text{Does the binomial fit the pattern?} &\qquad &\hspace{5mm} a^2−b^2 \\ &\text{Is this a difference?} &\qquad &\hspace{2mm} \text{____−____} \\ &\text{Are t...

$\begin{array} {llll} \textbf{Step 1.} &\text{Does the binomial fit the pattern?} &\qquad &\hspace{5mm} a^2−b^2 \\ &\text{Is this a difference?} &\qquad &\hspace{2mm} \text{____−____} \\ &\text{Are the first and last terms perfect squares?} & & \\ \textbf{Step 2.} &\text{Write them as squares.} &\qquad &\hspace{3mm} (a)^2−(b)^2 \\ \textbf{Step 3.} &\text{Write the product of conjugates.} &\qquad &(a−b)(a+b) \\ \textbf{Step 4.} &\text{Check by multiplying.} & & \end{array}$

1.2.EC: Exercises for Rational Expressions and Equations

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.EC%3A_Exercises_for_Rational_Expressions_and_Equations

8.

$\dfrac{3 x y^{2}}{8 y^{3}} \cdot \dfrac{16 y^{2}}{24 x}$ 9.

$\dfrac{72 x-12 x^{2}}{8 x+32} \cdot \dfrac{x^{2}+10 x+24}{x^{2}-36}$ 3.

$\dfrac{7 x^{2}}{x^{2}-9}+\dfrac{21 x}{x^{2}-9}$ 17. \(\d...8.

$\dfrac{3 x y^{2}}{8 y^{3}} \cdot \dfrac{16 y^{2}}{24 x}$ 9.

$\dfrac{72 x-12 x^{2}}{8 x+32} \cdot \dfrac{x^{2}+10 x+24}{x^{2}-36}$ 3.

$\dfrac{7 x^{2}}{x^{2}-9}+\dfrac{21 x}{x^{2}-9}$ 17.

$\dfrac{3 x}{x^{2}-9}+\dfrac{5}{x^{2}+6 x+9}$ 18.

$\dfrac{2 x}{x^{2}+10 x+24}+\dfrac{3 x}{x^{2}+8 x+16}$

$\dfrac{5 x^{2}+26 x}{(x+4)(x+4)(x+6)}$ 1.

$\dfrac{\dfrac{7 x}{x+2}}{\dfrac{14 x^{2}}{x^{2}-4}}$ 3.

$\dfrac{x-\dfrac{3 x}{x+5}}{\dfrac{1}{x+5}+\dfrac{1}{x-5}}$

1.2.4: Adding and Subtracting Polynomial Expressions

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.04%3A_Adding_and_Subtracting_Polynomial_Expressions

\[\begin{aligned}\left(x^{3}-2 x^{2} y\right.&+3 x y^{2}+y^{3} )+\left(2 x^{3}-4 x^{2} y-8 x y^{2}+5 y^{3}\right) \\ &=\left(x^{3}+2 x^{3}\right)+\left(-2 x^{2} y-4 x^{2} y\right)+\left(3 x y^{2}-8 x ...

$\begin{aligned}\left(x^{3}-2 x^{2} y\right.&+3 x y^{2}+y^{3} )+\left(2 x^{3}-4 x^{2} y-8 x y^{2}+5 y^{3}\right) \\ &=\left(x^{3}+2 x^{3}\right)+\left(-2 x^{2} y-4 x^{2} y\right)+\left(3 x y^{2}-8 x y^{2}\right)+\left(y^{3}+5 y^{3}\right) \\ &=3 x^{3}-6 x^{2} y-5 x y^{2}+6 y^{3} \end{aligned} \nonumber$

1.2.20: Adding, Subtracting, and Multiplying Radical Expressions

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.20%3A_Adding_Subtracting_and_Multiplying_Radical_Expressions

We call radicals with the same index and the same radicand like radicals to remind us they work the same as like terms. Remember that we always simplify radicals by removing the largest factor from th...We call radicals with the same index and the same radicand like radicals to remind us they work the same as like terms. Remember that we always simplify radicals by removing the largest factor from the radicand that is a power of the index.

$\sqrt[3]{27 n^{3}} \cdot \sqrt[3]{2 n^{2}}-\sqrt[3]{8 n^{3}} \cdot \sqrt[3]{2 n^{2}}$ Once we multiply the radicals, we then look for factors that are a power of the index and simplify the radical whenever possible.

1.3.E: Functions (Exercises)

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.03%3A_Inequalities_and_Functions/1.3.E%3A_Functions_(Exercises)

4) When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the

$x$ -axis from a reflection with respect to the

$y$ -axi...4) When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the

$x$ -axis from a reflection with respect to the

$y$ -axis? For the exercises 10-19, describe how the graph of the function is a transformation of the graph of the original function

$f$ . For the exercises 27-30, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.

2.27: Solving Equations in Quadratic Form

https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/02%3A_Algebra_Support/2.27%3A_Solving_Equations_in_Quadratic_Form

To factor the expression

$x^{4}-4 x^{2}-5$ , we noticed the variable part of the middle term is

$x^{2}$ and its square,

$x^{4}$ , is the variable part of the first term. (We know \(\left(x^{2}\rig...To factor the expression

$x^{4}-4 x^{2}-5$ , we noticed the variable part of the middle term is

$x^{2}$ and its square,

$x^{4}$ , is the variable part of the first term. (We know

$\left(x^{2}\right)^{2}=x^{4}$ .) So we let

$u=x^{2}$ and factored. Notice that in the quadratic equation

$ax^{2}+bx+c=0$ , the middle term has a variable,

$x$ , and its square,

$x^{2}$ , is the variable part of the first term.

1.5.9: Trigonometry Preview - Circles

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.05%3A_Exponential_and_Logarithmic_Functions/1.5.09%3A_Trigonometry_Preview_-_Circles

If we were to expand the equation in the previous example and gather up like terms, instead of the easily recognizable

$(x+2)^2 + (y-1)^2 = 4$ , we'd be contending with \(x^2 + 4x + y^2 - 2y + 1 = 0....If we were to expand the equation in the previous example and gather up like terms, instead of the easily recognizable

$(x+2)^2 + (y-1)^2 = 4$ , we'd be contending with

$x^2 + 4x + y^2 - 2y + 1 = 0.$ If we're given such an equation, we can complete the square to rewrite the equation in standard form for a circle. The diameter of the circle is the distance between the given points, so we know that half of the distance is the radius.

1.2.13: Simplifying, Multiplying, and Dividing Rational Expressions

https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.13%3A_Simplifying_Multiplying_and_Dividing_Rational_Expressions

\(

$\begin{array} {ll} &\dfrac{3a^2−8a−3}{a^2−25}·\dfrac{a^2+10a+25}{3a^2−14a−5} \\ & \\ \begin{array} {ll} \text{Factor the numerators and denominators} \\ \text{and then multiply.} \end{array}$ &\dfrac...\(

$\begin{array} {ll} &\dfrac{3a^2−8a−3}{a^2−25}·\dfrac{a^2+10a+25}{3a^2−14a−5} \\ & \\ \begin{array} {ll} \text{Factor the numerators and denominators} \\ \text{and then multiply.} \end{array}$ &\dfrac{(3a+1)(a−3)(a+5)(a+5)}{(a−5)(a+5)(3a+1)(a−5)} \\ & \\

$\begin{array} {l} \text{Simplify by dividing out} \\ \text{common factors.} \end{array}$ &\dfrac{\cancel{(3a+1)}(a−3)\cancel{(a+5)}(a+5)}{(a−5)\cancel{(a+5)}\cancel{(3a+1)}(a−5)} \\ & \\ \text{Simplify.} &\dfrac{(a−3)(a+5)}{(a−5)(a−5)} \\ & \\ \…

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