The features of the function g(x) = 4log(x) + 4 are
- (b) range (-∞, ∞)
- (d) x-intercept (0.1, 0)
- (e) Vertical asymptote, x = 0
How to determine the features of g(x)?
The function is given as;
g(x) = 4log(x) + 4
The intercept
A logarithmic function has no y-intercept.
Set g(x) to 0, to determine the x-intercept
4log(x) + 4 = 0
Divide through by 4
log(x) + 1 = 0
This gives
log(x) = -1
Take the inverse of both sides
x = 10^-1
Evaluate
x = 0.1
The x-intercept is (0.1, 0)
The vertical asymptote
Recall that:
A logarithmic function has no y-intercept.
This is so because it is undefined at x = 0
So, the vertical asymptote is x = 0
The domain and the range
A logarithmic function cannot take a negative input or 0 input
So, the domain is x > 0
However, the range is all set of real numbers i.e (-∞, ∞)
Hence, the features of g(x) are (b), (d) and (e)
Read more about function features at:
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