Advanced Algebra Semester Review

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What is a linear function?

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A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What does it mean for a function to have a zero?

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A zero of a function is a value of x for which the function's output is zero. In other words, it is the x-coordinate where the graph of the function intersects the x-axis.

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How do you find the y-intercept of a linear function?

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The y-intercept of a linear function is found by setting x = 0 in the function's equation and solving for y.

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What is the process for simplifying exponents?

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To simplify exponents, apply the laws of exponents, such as multiplying powers (add exponents), dividing powers (subtract exponents), and raising a power to a power (multiply exponents).

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What is the quadratic formula?

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The quadratic formula is used to find the solutions of a quadratic equation in the form ax^2 + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

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What does it mean to factor a polynomial?

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Factoring a polynomial involves expressing it as a product of its factors, which are polynomials of lower degrees. This helps in solving equations and simplifying expressions.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce based on its domain (input values).

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How do you determine the interval of a function's range?

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To determine the interval of a function's range, analyze the function's output values over its domain, often using graphing or calculus to find maximum and minimum values.

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What is the significance of the vertex in a quadratic function?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

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What are the steps to solve a quadratic equation by factoring?

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1. Write the equation in standard form (ax^2 + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for x.