Example 1

Solution to Example 1

• Since a point on the y axis has x coordinate equal to zero, to find the y interecpt, we set x to zero and find the y coordinate which is f(0).
  f(0) = -3(0) + 9 = 9
  
• A point on the x axis has y coordinate equal to 0, to find the x intercept, we set y = f(x) = 0 and solve for x
  f(x) = -3 x + 9 = 0
  
• Solve for x.
  x = 3
  
• The x and y intercepts of the graph of f are
  x intercept: (3 , 0)
  y intercept: (0 , 9)

Example 2

Solution to Example 2

• To find y intercept: Set x = 0 in the equation and solve for y.
  (0 - 1) ² + (y - 2) ² = 16
  
• Solve for y
  1 + (y - 2) ² = 16
  (y - 2) ² = 15
  solutions: y₁ = 2 + √(15) and y₂ = 2 - √(15)
  
• To find x intercept: set y = 0 in the given equation and solve for x
  (x - 1) ² + (0 - 2) ² = 16
  solutions: x₁ = 1 + √(12) and x₂ = 1 - √(12)
  
• The x and y intercepts of the graph of the given equation are
  x intercepts: A = (1 - √(12) , 0) and B = (1 + √(12) , 0)
  y intercepts: C = (0 , 2 - √(15)) and D = (0 , 2 + √(15))
  
• The graph shown below is that of the given equation. Examine the x and y intercepts and compare to those calculated. Note that the x and y intercepts may be determined graphically.
  
  

Example 3

Solution to Example 3

• Set x = 0 in the given equation and find the y intercept.
  3(0) + 2y = 6
  
• Solve for y
  y = 3
  
• Set y = 0 and solve for x to find the x intercept
  3 x + 2(0) = 6 , x = 2
  
• The x and y intercepts of the graph of the above equation are:
  x intercepts: A = (2 , 0)
  y intercepts: B = (0 , 3)
  
• The graph of the given equation is shown below. The x and y intercepts are those calculated above. Note that the x and y intercepts may be determined graphically.
  
  

Example 4

Solution to Example 4

• Set x = 0 in the formula of the given function and calculate the y intercept which is equal to f(0).
  y = f(0) = 3
  
• To find the x intercept: set y = f(x) = 0 and solve for x
  - x² + 2 x + 3 = 0
  Solutions: x₁ = -1 and x₂ = 3
  
• The x and y intercepts of the graph of the above equation are:
  x intercepts: A = (-1 , 0) and B = ( 3 , 0)
  y intercepts: C = (0 , 3)
  
• The graph of the given function is shown below along with the x and y intercepts as calculated above.
  
  

Example 5

Solution to Example 5

• Set x = 0 in the formula of the function and the y intercept is equal to f(0).
  y = f(0) = - ln(0 + 1) - 2 = - 2
  
• Set y = f(x) = 0 and solve for x
  - ln(x + 1) - 2 = 0
  ln(x + 1) = -2
  x + 1 = e^-2
  solution: x = - 1 + 1/e²
  
• The x and y intercepts of the graph of the above equation are:
  x intercepts: A = (-1+1/e² , 0)
  y intercepts: B = ( 0 , - 2)
  
• The graph of the given function is shown below along with the x and y intercepts as calculated above.
  
  

Example 6

Solution to Example 6

• The y intercept is equal to f(0).
  y = f(0) = e^{0 + 1} - 2 = e - 2
  
• Set y = f(x) = 0 and solve for x
  e^{x + 1} - 2 = 0
  e^{x + 1} = 2
  x + 1 = ln 2
  solution: x = - 1 + ln 2
  
• The x and y intercepts of the graph of the above equation are:
  x intercepts: A = (-1 + ln 2 , 0)
  y intercepts: B = ( 0 , e - 2)
  
• The graph of the given function and its x and y intercepts are shown below.
  
  

Example 7

Solution to Example 7

• The y intercept is equal to f(0).
  y = f(0) = 2/3
  
• Set the numerator of f(x) equal to zero and solve for x to find the x intercepts
  x ² - x - 2 = 0
  solution: x₁ = - 1 and x₂ = 2
  
• The x and y intercepts of the graph of the above function are:
  x intercepts: A = (-1 , 0) and B = (2 , 0)
  y intercepts: C = ( 0 , 2/3)
  
• The graph of the given function and the x and y intercepts are shown below.
  
  

Example 8

Solution to Example 8

• The y intercept is equal to f(0).
  y = f(0) = 1/2
  
• Set f(x) equal to zero and solve for x to fnd the x intercepts
  sin(x) + 1/2 = 0 , sin(x) = -1/2
  solution:Because of the periodicity of the sine function, there is an infinite number of x intercepts given by:
  x₁ = 7π/6 + 2kπ , k=0,~+mn~1 , ~+mn~2 , ...
  x₂ = 11π/6 + 2kπ , k=0,~+mn~1 , ~+mn~2 , ...
  
• Some of the x intercepts and the y intercept are:
  x intercepts: A = (-π/6 , 0) , B = (7π/6 , 0) and C = (11π/6 , 0)
  y intercepts: D = ( 0 , 1/2)
  
• The graph of the given function and the x and y intercepts are shown below.