Eight answers for six points, eh ? You're a tough businessman.
<span>F(x)=log(x/8)
X-intercept . . . the point where the function crosses the x-axis (f(x) is zero).
log(x/8) = zero
10^log(x/8) = 10^0 \/ \/ (x/8) = 1
x = 8
y-intercept . . . </span><span><span> the point where the function crosses the y-axis, ('x' is zero).</span>
Y = log(0/8)
= log( 0 )
= negative infinity.
Domain (everything that 'x' can be) . . . all positive numbers.
Range (everything that f(x) can be) . . . - inf to + inf . _______________________________________________________
First picture: f(x) = -3 / x⁴
To get an idea of what the asymptotes are, you have to draw the graph of the function, either on paper or in your mind. Think of what the function does, as 'x' drifts in from very far away on the left, crosses over zero, and drifts far away to the right.
'x' is very far away, negative . . . f(x) is positive, very small
'x' is negative 1 . . . . . f(x) = 3
'x' is close to zero, on the negative side . . . f(x) is positive, gigantic
'x' is close to zero, on the positive side . . . f(x) is negative, gigantic
'x' is very far away, positive . . . f(x) is negative, very small .
The horizontal asymptote is the x-axis. The vertical asymptote is the y-axis. _____________________________________________
