Parent Function, Domain, and Range:Each of the algebraic functions has there own trait that belong to each of the parent algebraic functions. To understands each of these unique and individual traits require an understanding of the parent function. This parent function expresses the domain and range that corresponds with the other parent functions.
y=x This is the parent function of linear functions. It also shows what the domain and range is. Domain: All Real Numbers Range: All Real Numbers (Slope is constant) |
Standard Form:One type of linear equation is the point slope form, which gives the slope of a line and the coordinates of a point on it. The point slope form of a linear equation is written as . In this equation, m is the slope and (x1, y1) are the coordinates of a point. Standard for is used to graph or find the x and y intercepts easily.
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Point-Slope Form:
The "point-slope" form of the equation of a straight line is:
y - y1 = m(x - x1)
Using this formula, when we know:
we can find other points on the line.
(x1, y1) is a known point
m is the slope of the line
(x, y) is any other point on the line
y - y1 = m(x - x1)
Using this formula, when we know:
we can find other points on the line.
(x1, y1) is a known point
m is the slope of the line
(x, y) is any other point on the line
Slope Intercept Form :
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You may already be familiar with the "y=mx+b" form.
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Slope, Midpoint, Distance:
Special Types:
Inequalities:
When you are graphing inequalities, you will graph the ordinary linear functions just like we done before. The difference is that the solution to the inequality is not the drawn line but the area of the coordinate plane that satisfies the inequality.
The linear inequality divides the coordinate plane into two halves by a boundary line (the line that corresponds to the function). One side of the boundary line contains all solutions to the inequality The boundary line is dashed for > and < and solid for ≥ and ≤. |
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