Linear parent function
f(x)=xDomain: {x| -∞ < x < ∞}Range: {y| -∞ < y < ∞}x & y intercept: (0,0)Max # of roots/zeros: 1Continuous
The linear parent function is a basic function that serves as a template for various linear equations. It is a straight line that passes through the origin with a slope of 1. The formula for the linear parent function is y = x.
The linear parent function can be used as a basis for finding the equation of a line given its slope and y-intercept. For example, if we know that a line has a slope of 2 and a y-intercept of 3, we can write the equation of the line using the linear parent function as follows:
y = mx + b (where m is the slope and b is the y-intercept)
y = 2x + 3
This equation represents a line with a slope of 2 and a y-intercept of 3, which intersects the y-axis at the point (0, 3).
The linear parent function can also be used to graph other equations. To graph an equation in the form y = mx + b, we can use the slope and y-intercept to plot two points on the line and then connect them with a straight line. For example, if we want to graph the line y = -2x + 5, we can use the slope of -2 and the y-intercept of 5 to plot two points on the line:
y = -2x + 5
When x = 0, y = 5. Plot the point (0, 5).
When y = 0, -2x + 5 = 0, x = 2.5. Plot the point (2.5, 0).
Then connect the two points with a straight line to graph the equation.
In summary, the linear parent function is a basic function that serves as a template for various linear equations. It can be used to find the equation of a line given its slope and y-intercept or to graph linear equations.
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