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Function Formulas

 

Function defines the relation between the input and the output. Function Formulas are used to calculate x-intercept, y-intercept and slope in any function. For a quadratic function you could also calculate its vertex. Also the function can be plotted in a graph for different values of x.
The x-intercept of a function is calculated by substituting the value of f(x) as zero. Similarly, the y-intercept of a function is calculated by substituting the value of x as zero. The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope. The vertex of a quadratic function is calculated by rearranging the equation to its general form, f(x) = a(x – h)2 + k; where (h,k) is the vertex.

Function Problems

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Some solved problems on functions are given below:

Solved Examples

Question 1: Calculate the slope, x-intercept and y-intercept of a linear equation, f(x) = 5x + 4 ?
Solution:

Given,
f(x) = 5x + 4

The general form of a linear equation is,
f(x) = mx + c
So,
Slope = m = 5

Substitute f(x) = 0,
0 = 5x + 4
5x = -4
x = $\frac{-4}{5}$
The x-intercept is ($\frac{-4}{5}$, 0)

Substitute x = 0,
f(x) = 5(0) + 4
f(x) = 0 + 4
f(x) = 4
The y-intercept is (0,4)

Question 2: Calculate the vertex, x-intercept and y-intercept of a quadratic equation, f(x) = x2 – 6x + 4 ?
Solution:

Given,
f(x) = x2 – 6x + 4
f(x) = (x2 – 6x + 9) – 5
f(x) = (x – 3)2 – 5

The general form of a linear equation is,
f(x) = (x – h)2 + k
So,
Vertex = (h,k) = (3,-5)

Substitute f(x) = 0,
0 = x2 – 6x + 4
x2 – 6x + 4 = 0
x = 6 ± $\frac{\sqrt{(-6)^{2}-4(1)(4)}}{2(1)}$

x = 6 ± $\frac{\sqrt{36-16}}{2}$

x = 6 ± $\frac{\sqrt{20}}{2}$

x = 6 ± $\frac{2\sqrt{5}}{2}$

x = 6 ± $\sqrt{5}$

The given quadratic function has two x-intercepts.
The x-intercepts are (6 – $\sqrt{5}$, 0) and (6 + $\sqrt{5}$, 0)

Substitute x = 0,
f(x) = (0)2 – 6(0) + 4
f(x) = 0 + 0 + 4
f(x) = 4
The y-intercept is (0,4)

More topics in Function Formula
Average Rate of Change Formula Simpson’s Rule Formula
Linear Approximation Formula Quadratic Function Formula
Linear Function Formula Inverse Function Formula
Maclaurin Series Formula
Related Formulas
Sampling Error FormulaRiemann Sum Formula
Magnitude of a Vector FormulaLaw of Cosines Formula
Regular Tetrahedron FormulaPartial Differential Equations
Surface Area of a Rectangular Prism FormulaMidpoint Formula