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Questions and Answers
List the intercepts for the graph of the equation. x² + y - 36 = 0
List the intercepts for the graph of the equation. x² + y - 36 = 0
(-6, 0), (0, 36), (6, 0)
List the intercepts for the graph of the equation. 16x² + y² = 16
List the intercepts for the graph of the equation. 16x² + y² = 16
(-1, 0), (0, -4), (0, 4), (1, 0)
List the intercepts for the graph of the equation. y = x² + 14x + 48
List the intercepts for the graph of the equation. y = x² + 14x + 48
(-8, 0), (-6, 0), (0, 48)
Find an equation for the line, in the indicated form, with the given properties. Containing the points (-2, 2) and (7, -4); slope-intercept form
Find an equation for the line, in the indicated form, with the given properties. Containing the points (-2, 2) and (7, -4); slope-intercept form
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Write an equation for the line described. Write the equation in the form specified. Through (3, 4), parallel to y + 8x = 4
Write an equation for the line described. Write the equation in the form specified. Through (3, 4), parallel to y + 8x = 4
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Find an equation for the line with the given properties. Perpendicular to the line y = 1/9x + 9; containing the point (4, -5)
Find an equation for the line with the given properties. Perpendicular to the line y = 1/9x + 9; containing the point (4, -5)
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Write the standard form of the equation of the circle with radius r and center (h, k). r = 10; (h, k) = (1, -9)
Write the standard form of the equation of the circle with radius r and center (h, k). r = 10; (h, k) = (1, -9)
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Write the standard form of the equation of the circle with radius r and center (h, k). r = √17; (h, k) = (-9, 8)
Write the standard form of the equation of the circle with radius r and center (h, k). r = √17; (h, k) = (-9, 8)
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Find the center (h, k) and radius r of the circle with the given equation. (x - 6)² + (y + 9)² = 144
Find the center (h, k) and radius r of the circle with the given equation. (x - 6)² + (y + 9)² = 144
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Find the center (h, k) and radius r of the circle with the given equation. x² + y² - 6x - 16y + 73 = 16
Find the center (h, k) and radius r of the circle with the given equation. x² + y² - 6x - 16y + 73 = 16
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Find the value for the function. Find f(-2) when f(x) = (x^2 - 4)/(x + 3)
Find the value for the function. Find f(-2) when f(x) = (x^2 - 4)/(x + 3)
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Find the domain of the function. h(x) = (x - 3)/√(x² - 81x)
Find the domain of the function. h(x) = (x - 3)/√(x² - 81x)
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Find the domain of the function. f(x) = x² + 4
Find the domain of the function. f(x) = x² + 4
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Find the domain of the function. f(x) = √7 - x
Find the domain of the function. f(x) = √7 - x
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Use the graph of f given below to find f(40).
Use the graph of f given below to find f(40).
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Determine algebraically whether the function is even, odd, or neither. f(x) = -3x^4 - x^2
Determine algebraically whether the function is even, odd, or neither. f(x) = -3x^4 - x^2
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Determine algebraically whether the function is even, odd, or neither. f(x) = 4x^3 + 5
Determine algebraically whether the function is even, odd, or neither. f(x) = 4x^3 + 5
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Determine algebraically whether the function is even, odd, or neither. f(x) = x/(x^2 - 3)
Determine algebraically whether the function is even, odd, or neither. f(x) = x/(x^2 - 3)
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Use the graph to find the intervals on which it is increasing, decreasing, or constant.
Use the graph to find the intervals on which it is increasing, decreasing, or constant.
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Find the average rate of change for the function between the given values. f(x) = 4x^3 - 8x^2 - 1; from 1 to 5
Find the average rate of change for the function between the given values. f(x) = 4x^3 - 8x^2 - 1; from 1 to 5
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Study Notes
Final Exam Review - Math 1314
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Intercepts: Find the x and y intercepts for various equations.
- Example equations: x² + y - 36 = 0, 16x² + y² = 16, y = x² + 14x + 48.
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Line Equations: Find equations of lines:
- Write equations in slope-intercept form given points or properties like parallel lines.
- Find equations of lines perpendicular to a given line and containing a specific point.
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Circle Equations: Find standard form of a circle given radius and center.
- Find the center and radius of a circle given the equation.
- Example: (x - 6)² + (y + 9)² = 144
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Function Evaluation: Find the value of a function at a given input (x-value).
- Example: Find f(-2) when f(x) = (x² - 4)/(x + 3)
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Function Domain: Find the domain of a function
- Example: h(x) = (x - 3)/(x³ − 81x)
- Function Graph Analysis: Analyze function graphs to determine intervals of increase, decrease, or constant behavior and find f(40) or related problems from graph.
- Even/Odd Functions: Determine if functions are even, odd, or neither algebraically.
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Average Rate of Change: Calculate the average rate of change of a function over a given interval.
- Example: f(x) = 4x³ - 8x² - 1; from 1 to 5
- Composite Functions: Evaluate composite functions and use graphs or information to find the value of composite function -Example: f(x) = 2x + 2, g(x) = 2x² + 1; find (f°g)(0).
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Transformation of functions Use transformation to sketch the graphs of new functions from a given function
- Example: F(x) =f(x+2) - 1
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Horizontal Asymptotes (and Rational Functions): Find the equation of the horizontal asymptote of a rational function.
- Example: g(x) = (x + 7)/(x² - 36)
- Graph of function: Answer questions about a function from its graph. -Example: For what numbers x is f(x) > 0?
- Inverse Functions: Find the inverse of a given one-to-one function.
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Logarithms: Convert expressions between exponential and logarithmic forms.
- Simplify expressions involving logarithms. Find the domain of a logarithmic function
- Exponential Equations: Solve exponential equations.
- Systems of Equations: Solve a system of linear equations using matrices.
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Description
Prepare for your Math 1314 final exam with this comprehensive review quiz covering intercepts, line equations, circles, function evaluation, and domain analysis. Test your knowledge with example problems and refine your understanding of key mathematical concepts essential for success. Boost your confidence as you tackle various equations and function graph analysis.
