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Questions and Answers
For the relation given, does the first set of inputs and outputs define a function? Explain your reasoning.
For the relation given, does the first set of inputs and outputs define a function? Explain your reasoning.
No, it does not define a function because the input '3' is associated with multiple outputs.
What is the value of f(-a) for the function $f(x) = \sqrt{x - 2}$?
What is the value of f(-a) for the function $f(x) = \sqrt{x - 2}$?
The value is $\sqrt{-a - 2}$.
Using the x-intercept method, identify one real solution of the equation: $x^3 + 10x^2 + 27x + 18 = 0$.
Using the x-intercept method, identify one real solution of the equation: $x^3 + 10x^2 + 27x + 18 = 0$.
One solution is $x = -2$.
What are the solutions of the equation $x^2 - 4x - 5 = 0$?
What are the solutions of the equation $x^2 - 4x - 5 = 0$?
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Solve the equation $-3x^2 + 8x - 4 = 0$ for x.
Solve the equation $-3x^2 + 8x - 4 = 0$ for x.
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What is the solution to the equation $3(x + 1)^2 - 36 = 0$?
What is the solution to the equation $3(x + 1)^2 - 36 = 0$?
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What is the domain of the function $h(x) = \frac{4x}{x(x^2 - 81)}$?
What is the domain of the function $h(x) = \frac{4x}{x(x^2 - 81)}$?
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Express the solution to the inequality $-10 \leq 2x - 4 \leq 0$ in interval notation.
Express the solution to the inequality $-10 \leq 2x - 4 \leq 0$ in interval notation.
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Determine the x-intercepts of the quadratic function $f(x) = x^2 + 7x + 10$. What is the vertex of this graph?
Determine the x-intercepts of the quadratic function $f(x) = x^2 + 7x + 10$. What is the vertex of this graph?
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If the parent function is $f(x) = x^2$, what is the new rule for the function after translating it 4 units right and 3 units up?
If the parent function is $f(x) = x^2$, what is the new rule for the function after translating it 4 units right and 3 units up?
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Write the vertex form of the function $f(x) = -3x^2 + 12x - 7$. What is the vertex?
Write the vertex form of the function $f(x) = -3x^2 + 12x - 7$. What is the vertex?
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Calculate $h(2+t)$ for the function $h(t) = t^3 + 3t$. What is the resulting polynomial?
Calculate $h(2+t)$ for the function $h(t) = t^3 + 3t$. What is the resulting polynomial?
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For the function $f(x) = -2x$, what is the average rate of change between $x = 1$ and $x$?
For the function $f(x) = -2x$, what is the average rate of change between $x = 1$ and $x$?
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Using the Remainder Theorem, what is the remainder when dividing $f(x)$ by $x - c$?
Using the Remainder Theorem, what is the remainder when dividing $f(x)$ by $x - c$?
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What is the maximum number of zeros a polynomial function can have and how can Descartes' Rule of Signs be applied?
What is the maximum number of zeros a polynomial function can have and how can Descartes' Rule of Signs be applied?
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List the potential rational zeros of a polynomial function without finding the actual zeros.
List the potential rational zeros of a polynomial function without finding the actual zeros.
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Study Notes
PreCalculus Final Exam - December 2024
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Multiple Choice Questions (1-6): Focuses on identifying functions, evaluating functions, solving quadratic equations and finding real solutions.
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Question 1: Assess the concept of relations being functions through tables.
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Question 2: Calculate f(-a) for a given function f(x).
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Question 3: Find real solutions of cubic equations using the x-intercept method.
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Question 4: Solve quadratic equations using various methods; find solutions for x²-4x-5=0.
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Question 5: Solve quadratic equations; focus on example -3x² + 8x − 4 = 0
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Question 6: Solve equations by taking square roots. Example: 3(x+1)² - 36 = 0
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Question 7: Solve equations; example focused on 7x = 2x² + 1
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Question 8: Find real solutions to quadratic equations; example focused on (x²-7x-8)=0/(x-8).
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Question 9: Find all real solution to equations including absolute values. example focused on 4x - 7 + √4x-14=11
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Question 10: Find real solutions; including rational numbers; example focused on (6/5)-x +6 +2 = 10/5
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Question 11: Graphically depict inequalities 3≤x<6
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Question 12: Solve and express solution in interval notation -10≤2x-4≤0
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Question 13: Identify relations that are not functions.
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Question 14: Determine the domain of a function; example focused on 4x/x(x2-81)
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Question 15: Find the domain h(x) = x2+√x+11
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Question 16: Graphically determine whether graphs represent functions.
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Question 17-21: Focuses on finding local maxima and minima, x intercepts and vertex of quadratic functions, finding rules of transformations, graphing functions.
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Question 22: Determine the domain of a function based on its graph.
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Question 23: Given a function h(t) = t³ + 3t ; solve for h(2+t) .
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Question 24: Find the average rate of change of f from 1 to x Given f(x) = -2x
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Question 25: Calculate average rate of change for different values and functions.
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Questions 26-32: Focuses on polynomial functions, finding remainders, and solving equations and determining maximum number of zeros.
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Description
This quiz covers essential precalculus concepts, including functions, quadratic equations, and cubic equations. Students will evaluate functions, solve various types of equations, and identify real solutions. It's an excellent review tool for mastering precalculus topics ahead of the final exam.
