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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
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
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)
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)
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)
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
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
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)
Find the domain of the function. h(x) = (x - 3)/√(x² - 81x)
Find the domain of the function. h(x) = (x - 3)/√(x² - 81x)
Find the domain of the function. f(x) = x² + 4
Find the domain of the function. f(x) = x² + 4
Find the domain of the function. f(x) = √7 - x
Find the domain of the function. f(x) = √7 - x
Use the graph of f given below to find f(40).
Use the graph of f given below to find f(40).
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
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
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)
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.
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
Flashcards
x-intercepts
x-intercepts
Points where the graph crosses the x-axis. Y-coordinate is always 0.
y-intercepts
y-intercepts
Points where the graph crosses the y-axis. X-coordinate is always 0.
Slope-intercept form
Slope-intercept form
Equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.
Parallel lines
Parallel lines
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Perpendicular lines
Perpendicular lines
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Standard form of a circle
Standard form of a circle
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Finding the center and radius of a circle
Finding the center and radius of a circle
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Function evaluation
Function evaluation
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Domain of a function
Domain of a function
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Even function
Even function
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Odd function
Odd function
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Increasing function
Increasing function
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Decreasing function
Decreasing function
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Average rate of change
Average rate of change
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Piecewise function
Piecewise function
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Transformations of functions
Transformations of functions
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Vertex of a parabola
Vertex of a parabola
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Axis of symmetry of a parabola
Axis of symmetry of a parabola
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Maximum height of a projectile
Maximum height of a projectile
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Maximum revenue
Maximum revenue
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Solving inequalities
Solving inequalities
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Zero of a polynomial function
Zero of a polynomial function
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Multiplicity of a zero
Multiplicity of a zero
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Factor Theorem
Factor Theorem
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Potential rational zeros of a polynomial
Potential rational zeros of a polynomial
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Vertical asymptote
Vertical asymptote
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Horizontal asymptote
Horizontal asymptote
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Composite function
Composite function
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Inverse function
Inverse function
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Logarithmic expression
Logarithmic expression
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Domain of a logarithmic function
Domain of a logarithmic function
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Properties of logarithms
Properties of logarithms
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Study Notes
Final Exam Review - Math 1314
- Intercepts: Find the x and y intercepts for various equations.
- Example equations: x² + y - 36 = 0, 16x² + y² = 16, y = x² + 14x + 48.
- 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.
- 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
- 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)
- 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.
- 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).
- Transformation of functions Use transformation to sketch the graphs of new functions from a given function
- Example: F(x) =f(x+2) - 1
- 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.
- 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.
