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What is the rule for multiplying two expressions with the same base?
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Add the exponents of the expressions (e.g., x^2 * x^5 = x^7).
When solving linear inequalities, under what condition must you flip the inequality sign?
You must flip the sign when multiplying or dividing both sides of an inequality by a negative number.
How do you handle negative exponents when simplifying fractions?
Move the base with the negative exponent to the other side of the fraction (e.g., x^4 / x^7 = 1/x^3).
Explain how to solve an inequality that includes absolute values.
Split the inequality into two scenarios to handle the possible positive and negative outcomes, then solve each separately.
In polynomial simplification, why is it important to combine like terms?
Combining like terms simplifies the expression and makes it easier to evaluate or use in further calculations.
What must be checked when using function notation, f(x)?
Ensure that the input x is within the domain of the function, where the function is defined and can be evaluated.
How can graphing help in solving a system of equations?
Graphing can illustrate the system's solution by showing where lines intersect, representing a common solution.
What transformation is represented by the vertex form of a quadratic function, y = a(x-h)^2 + k?
The vertex form indicates horizontal shifts by h, vertical shifts by k, and stretches or compressions based on a.
What does the term 'composition of functions' refer to?
Composition of functions refers to applying one function to the results of another, denoted as f(g(x)) or g(f(x)).
How are systems of linear equations solved using the elimination method?
Align equations to eliminate a variable by adding or subtracting them, allowing you to solve for the remaining variables.
Describe the process of completing the square in solving quadratic equations.
Rearrange the equation, take half the coefficient of x, square it, and add to both sides to transform into a perfect square trinomial.
What is the significance of the zero exponent rule?
Any base raised to the zero exponent equals one.
Describe how to graph a linear equation in slope-intercept form.
Plot the y-intercept on the y-axis and use the slope to find other points on the line; draw the line through these points.
What is the FOIL method and when is it used?
The FOIL Method is used to multiply two binomials. It stands for First, Outer, Inner, Last.
What is the quadratic formula, and for what type of equations is it used?
The quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), is used to find solutions of quadratic equations.
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