College Algebra Final Exam Questions and 100% Complete Verified Solutions 2024/2025, Exams of Algebra

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College Algebra Final Exam Questions and

100% Complete Verified Solutions

2024/

Domain set of all first components of an ordered pair (x,y) - the x Range set of all second components of an ordered pair (x,y)- the y Vertical Line Test a test for determining whether a graph will define y as a function of x Zeros of a Function the x-values for which f(x)= To find x-intercepts on a graph look for the points at which the graph crosses the x-axis To find y-intercepts on a graph look for the point at which the graph crosses the y-axis Even Functions if the right side of the equation of an even function does not change if x is replaces with - x. Odd Functions if every term on the right side of the equation changes sign if x is replaced with - x The Slope of a Line rise/run change in y/change in x How to find the slope of a line y2-y1/x2-x Point Slope Equation y-y1=m(x-x1) Slope- Intercept Equation y=mx+b

Horizontal Line Equation y= Vertical Line Equation x= General Form of the Equation of a Line Ax+By+C= Parallel Lines Two nonintersecting lines that lie in the same plane. Since two parallel lines have the same 'steepness; they have the same Slope Perpendicular Lines Two lines that intersect at a right angle One line perpendicular to another line if its slope is the negative reciprocal of the slope of another line Vertical Shifts- Upward the graph of y=f(x)+c is the graph of y=f(x) shifted c units vertically upward Vertical Shifts- Downward the graph of y=f(x)-c is the graph of y=f(x) shifted c units vertically downward Horizontal Shift- Left the graph of y=f(x+c) is the graph of y=f(x) shifting to the left c units Horizontal Shift- Right the graph of y=f(x-c) is the graph of y=f(x) shifting to the right c units Reflection about the x-axis the graph of y=-f(x) is the graph of y=f(x) reflected about the x-axis Reflection about y-axis the graph of y=f(-x) is the graph of y=f(x) reflected about the y-axis Sum of Functions (f+g)(x)=f(x)+g(x) Difference of Functions (f-g)(x)=f(x)-g(x) Product/Multiplying of Functions (fg)(x)=f(x)*g(x) Quotient/Dividing of functions (f/g)(x)=f(x)/g(x) To find the inverse of a fuction to solve, you replace f(x) with y, then you interchange x and y, then solve for y