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Domain 1: AlgebraLinear EquationsSOLVINGNUMBER OF SOLUTIONSLinear Functions: GraphsSLOPE-INTERCEPT FORMPARALLEL AND PERPENDICULAR LINESSTANDARD FORMFUNCTION NOTATIONTRANSFORMATIONSLinear Functions: Creating and InterpretingINPUTS AND OUTPUTSSLOPE-INTERCEPT FORMSTANDARD FORMSystems of Linear EquationsSOLVINGNUMBER OF SOLUTIONSLinear Inequalities and SystemsLINEAR INEQUALITIES IN ONE VARIABLELINEAR INEQUALITIES IN TWO VARIABLESSYSTEMS OF LINEAR INEQUALITIES

Domain 1: AlgebraLinear Functions: GraphsFunction NotationIntroduction to function notationAny linear equation in two variables is a function. The function notation f(x) represents the value of the function f when the input is x. Therefore, a linear equation in terms of input x and output y represents a linear function f where y = f(x).Note: Some other common names of functions are g(x) and h(x).Exampleg(x) = −10x + 2What is the value of g(4)? For what value of x does g(x) = 12?

Domain 1: AlgebraPoints on a graphThe function notation f(c) = d means the graph of function f passes through the point (c, d) in the xy-plane. ExampleIn the xy-plane, the y-coordinate of the y-intercept of the graph of the function h is k. Which of the following must be equal to k?A)h(−1)B)h(0)C)h(1)Explanation:The y-intercept is the point where the graph intersects the y-axis. This point has x-value 0. When the input of function h is 0, the output is h(0). This means the y-intercept is (0, h(0)). It is given that the y-coordinate of the y-intercept of function h is k, so the y-intercept is (0, k).Therefore, k is equal to h(0).Tactic: A y-intercept has input 0, so f(0) represents the y-intercept for any function f in the xy-plane.

Domain 1: AlgebraExampleIn the linear function f, f(0) = 6 and f(1) = 11. Which equation defines f?A) f(x) = 11x + 6B) f(x) = 5xC) f(x) = 5x + 11D) f(x) = 5x + 6Explanation:The function notation f(c) = d means that the function f has an output of d when x = c, and the graph of y = f(x) contains the point (c, d). It is given that f(0) = 6 and f(1) = 11, so the line contains the points (0, 6) and (1, 11).Each equation from the choices is in slope-intercept form f(x) = mx + b, where m is the slope andb is the y-intercept. Use the two known points to find m and b.slope m Plug the points (x1, y1) = (0, 6) and (x2, y2) = (1, 11) into the slope formula and simplify.m=y2− y1x2− x1Slope formulam=11−61−0Plug in (x1, y1) = (0, 6)and (x2, y2) = (1, 11)m=51SubtractThe slope m is 5. y -intercept b The point (0, 6) has x-coordinate 0, so it is the point where the graph intersects the y-axis and the y-intercept b is 6. Plug m = 5 and b = 6 into f(x) = mx + b.f(x) = mx + b Slope-intercept formf(x) = 5x + 6 Plug in m = 5 and b = 6Therefore, the equation that defines linear function f is f(x) = 5x + 6.

Domain 1: AlgebraExampleFor the linear function g, the table shows three values of x and their corresponding values of g(x). Which equation defines g(x)?A) g(x) = 5x + 22B) g(x) = 22x + 27C) g(x) = 27x + 31Explanation:Each equation from the choices is in slope-intercept form g(x) = mx + b, where m is the slope and b is the y-intercept. Use the values in the given table to calculate the slope m and y-intercept bfor g(x).slope m The slope m of a line that represents a function f is equal to the change in f(x) divided by the corresponding change in x.Each row in the table represents a pair of corresponding values of x and g(x). Find the change in g(x) and the corresponding change in x for any two rows and divide to calculate the slope m.The slope m is 5.

Domain 1: Algebray -intercept b The y-intercept is the function value at the point where a graph intersects the y-axis and has x-value 0. Identify from the table that when x = 0, the value of f(x) is 22. Therefore, the y-intercept b is 22.Plug m = 5 and b = 22 into g(x) = mx + b.g(x) = mx + b Slope-intercept formg(x) = 5x + 22 Plug in m = 5 and b = 22Therefore, an equation that defines the linear function g is g(x) = 5x + 22.

Domain 1: AlgebraLinear Functions: GraphsTransformationsCheck for Understanding1. The function d is defined by d(s) = 11s − 67. What is the value of d(5)?2. The function h is defined by h(x)=−12x−34. For what value of x does h(x)=−49?3. In the linear function g, g(0) = −6 and g(5) = −3. Which equation defines g?A)g(x)=−3 x−6B)g(x)=35x−6C)g(x)=35xD)g(x)=53x−6