f(x) = 2x+1
y = 2x + 1
In solving function and for the purpose of graphing, you have to find the following:
a) the roots/zeros
b) x- and y- intercepts
c) interval
d) domain and range
a) To find the roots/zeros, set y to 0:
2x + 1 = 0
2x = -1
2x/2 = -1/2
x = -1/2, the solution is {-∞ <x<∞}
b) When x = -1/2 and y = 0
The coordinates of x-intercept is (-1/2,0)
To get y-intercept:
y = mx+b
y = 2x + 1
y - intercept = 1
The coordinates of y-intercept is (0,1)
c) This is linear function, and there is no undefined range, therefore the interval is ( -∞, +∞).
d) The domain and range have the same interval for reason mentioned in in (c), therefore the domain and range are:
Domain (x) = {x/x ∈ R}
Range (y) = {y/y ∈ R}
