find the x and y intercepts of f(x) = x^2 -16/ x^2 - 4
obtain additional points ?
x intercept, when f(x)=0
x must be 4 for that. Intercept (4,0)
y intercept, when x=0
f(x)=4 (o,4)
ok thanks
To find the x-intercepts of a function, we need to solve the equation f(x) = 0. Similarly, to find the y-intercept, we substitute x = 0 into the equation f(x). Let's go step by step:
1. To find the x-intercepts, we set f(x) = 0:
x^2 - 16 / x^2 - 4 = 0
To make this equation simpler, we can multiply both sides of the equation by (x^2 - 4) to eliminate the denominator:
(x^2 - 4)(x^2 - 16) / (x^2 - 4) = 0
Simplifying, we get:
(x^2 - 16) = 0
Now, we have a quadratic equation that can be factored:
(x + 4)(x - 4) = 0
Setting each factor equal to zero, we have:
x + 4 = 0 or x - 4 = 0
Solving these equations, we get:
x = -4 or x = 4
Therefore, the x-intercepts of the function f(x) = x^2 - 16 / x^2 - 4 are x = -4 and x = 4.
2. To find the y-intercept, we substitute x = 0 into the equation f(x):
f(0) = (0^2 - 16) / (0^2 - 4)
Simplifying, we get:
f(0) = -16 / -4
= 4
Therefore, the y-intercept of the function f(x) = x^2 - 16 / x^2 - 4 is y = 4.
3. To obtain additional points on the graph of the function, we can choose different values of x and substitute them into the equation f(x) = x^2 - 16 / x^2 - 4. For example, we can choose x = -3 and x = 3:
f(-3) = (-3^2 - 16) / (-3^2 - 4)
= (-9 - 16) / (9 - 4)
= (-25) / (5)
= -5
Therefore, the point (-3, -5) is an additional point on the graph of the function f(x) = x^2 - 16 / x^2 - 4.
f(3) = (3^2 - 16) / (3^2 - 4)
= (9 - 16) / (9 - 4)
= (-7) / (5)
Therefore, the point (3, -7/5) is another additional point on the graph of the function f(x) = x^2 - 16 / x^2 - 4.
By following these steps, you can find the x and y-intercepts of the function and obtain additional points on its graph.