How to Find x and y Intercepts Of Graphs?

How to find the x and the y intercepts of graphs of functions and equations?
The x and y intercepts of a graph are points of intersection of the graph with the x axis and the y axis respectively. This is a tutorial with examples and detailed solutions on how to find these points.

Example 1

Find the x and the y intercepts of the graph of function f defined by \[ f(x) = - 3 x + 9 \]

Solution to Example 1

Example 2

Find the x and the y intercepts of the graph of the circle given by the equation: \[ (x - 1)^2 + (y - 2)^2 = 16 \]

Solution to Example 2

Example 3

Calculate the x and the y intercepts of the graph of the linear equation given by \[ 3x + 2y = 6 \]

Solution to Example 3

Example 4

Calculate the \(x\)- and \(y\)-intercepts of the graph of the quadratic function given by

\( f(x) = -x^2 + 2x + 3 \)

Solution to Example 4

graph of given equation in example 4

Example 5

Determine the \(x\) and the \(y\) intercepts of the graph of the logarithmic function given by \[ f(x) = -\ln(x + 1) - 2 \]

Solution to Example 5

graph of given equation in example 5

Example 6

Calculate the \(x\) and the \(y\) intercepts of the graph of the exponential function given by: \[ f(x) = e^{x + 1} - 2 \]

Solution to Example 6

graph of given equation in example 6

Example 7

Calculate the x and the y intercepts of the graph of the rational function given by

\[ f(x) = \frac{x^2 - x - 2}{x^2 - x - 3} \]

Solution to Example 7

graph of given equation in example 7

Example 8

Calculate the \( x \) and the \( y \) intercepts of the graph of the sine function given by \[ f(x) = \sin(x) + \frac{1}{2} \]

Solution to Example 8

graph of given equation in example 8