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Information on various basic graph functions including linear, quadratic, cubic, square root, rational, absolute value, exponential, and logarithmic functions. Each function includes its domain, range, x and y intercepts, increasing and decreasing properties, and examples of shifted graphs with shifting instructions. This worksheet is useful for students studying mathematics, particularly those focusing on algebra and calculus.
Typology: Assignments
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Basic Linear Function: f (x) x Domain: (^ ,^ ) Range: (^ ,^ ) x intercept: (0, 0) y intercept: (0, 0) Increasing everywhere. This function is one-to-one. Example of a shifted graph: 3f (x^ ^ 2)^ ^1 shifting instructions: stretched by 3, left 2, down 1 new formula: y^ 3x^ ^5 try to get this yourself by working with the shifting instructions! Domain: (^ ,^ ) Range: (^ ,^ ) x intercept: (5/3, 0) y intercept: (0, 5)
Basic Quadratic function: f (x) x^2 Domain: (^ ,^ ) Range: [0,^ ) x intercept: (0, 0) y intercept: (0, 0) Decreasing: (^ ,0) Increasing: (0,^ ) This function is not one-to-one. Example of a shifted graph: f (x^ ^ 2)^ ^9 shifting instructions: left 2, down 9 new formula: 2 f (x) x 4x 5 Domain: (^ ,^ ) Range: [ 9,^ ) x intercepts: (5, 0) and (1, 0) y intercept: (0, 5) track the key point (0, 0) to (2, 9)
Basic Cube Root function: 3 1 f (x)^3 xx Domain: (^ ,) Range: (^ ,) x intercept: (0, 0) y intercept: (0, 0) Increasing everywhere. This function is one-to-one. Example of a shifted graph: f(x + 1) 2 shifting instructions: left 1, down 2 new formula: (^) f (x) (x 1 ) (^32) 1 Domain: (^ ,) Range: (^ ,) x intercept: (7, 0) y intercept: (0, 1) track the key point (0, 0) to (1, 2)
Basic Square Root function: 2 1 f (x) x x Domain: (^ ,) Range: [^0 ,) x intercept: (0, 0) y intercept: (0, 0) Increasing on its domain. This function is one-to-one. Example of a shifted graph: f(3 x) shifting instructions: reflect about the x axis, left 3, reflect about the y axis new formula: f^ (x)^3 x Domain: (,^3 ] Range: [^0 ,) x intercept: (3, 0) y intercept: ( 0 . 3 )
Basic Absolute Value function: f (x) x Domain: (^ ,) Range: [^0 ,) x intercept: (0, 0) y intercept: (0, 0) Decreasing: (^ ,0) Increasing: (0,^ ) This function is not one-to-one. Example of a shifted graph: f(x 5) + shifting instructions: reflect about the x axis, right 5, up 2 new formula: f^ (x) x^5 ^2 Domain: (^ ,) Range: (,^2 ] x intercepts: (7, 0) and (3, 0) y intercept: (0, 3)
Basic exponential function: x f (x) b b 1, Domain: (^ ,) Range: (0,^ ) x intercept: none y intercept: (0, 1) horizontal asymptote: y = 0 Increasing everywhere. (illustration is with b = 3) Example of a shifted graph: f(x + 3) + 9 shifting instructions: reflect about the x axis, left 3, up 9, new formula: f (x) 3 x ^3 9 Domain: (^ ,) Range: (^ ,9) x intercept: (1, 0) y intercept: (0, 18)) horizontal asymptote: y = 9 Be sure to know how to handle this if b = e.
