Types of Functions
The graph of a linear function is in the shape of a...
Line
x(x) =
x2
Solve the following equation (Hint: set each factor equal to 0 and solve for x)
0=(x-1)(x+1)
x = 1 and x = -1
x2(x2)
x4
(2x + 2) + (3x + 3)
Is the following function linear, quadratic, or exponential?
f(x) = x2+4x-6
Quadratic
y(y+4)
y2+4y
9 = x2 (Hint: There are TWO solutions)
x = 3 and x = -3
x0
1
(3x - 1) - (2x +1)
x - 2
The graph of a quadratic function is in the shape of a...
Parabola
t2+2t-3
Solve the following quadratic equation:
0 = x2+7x+10
Factors are (x+2)(x+5)
x = -2 and x = -5
y3x/y
y2x
(3x2+2x-10) + (2x2-2x-5)
5x2-15
Is the following equation linear, quadratic, or exponential?
g(t) = t(t-16)
Quadratic
(x+3)(x2+3x+4)
x3+6x2+13x+12
Solve the following:
0 = (3x+2)(6x-12)
x = -2/3 and x = 2
y2/3 in exponent form is...
y2 with a radical of index 3
(3x+x2-5) + (-2x2+2x+2)
-x2+5x-3
If you are given a table of values, how do you know if the function is linear, quadratic, or exponential? Be as detailed as possible.
Check the first and second difference of the output values. If the 1st difference is constant, it is linear. If the 2nd difference is constant, it is quadratic.
Bonus points: Exponential has a constant ratio
(x2+3x+1)(2x2-x+3)
2x4+5x3+2x2+8x+3
4=x2-13x+34
factors are (x-10)(x-3),
solutions are x = 10 and x = 3
(y-3x5)2/(y-7x9)
yx
(3 - 4x3 + 2x) - (4x2 - 3x + 3x3)
-7x3-4x2+5x+3