Question

Identity the key features of the exponential function(x) = 5* and its graph by completing each sentence:

Answer 1

Answer:

Domain: - ∞ < x < ∞

Range: y > 0

Asymptote: y = 0

y-intercept: 1

Step-by-step explanation:

The DOMAIN is the set of possible input values, so in this case it is the set of possible x values.  For this function the set of input values is not restricted, so this is why we say that the domain can be ANY value by denoting it as - ∞ < x < ∞.  Another way of stating this would be to say

x ∈ R, which means x belongs to the set of real numbers. Real numbers are any number (positive, negative, zero, irrational, rational, whole etc.) except imaginary numbers.

The RANGE is the set of values the function takes, i.e. the output.  As this function is an exponential function, the function is always positive.  Hence the range is y > 0 or f(x) > 0.

An ASYMPTOTE is a line that the curve approaches, as it heads towards infinity (or negative infinity).  Asymptotes can be horizontal, vertical or oblique.   For this function, there is a horizontal asymptote at y = 0:  this is because as x tends to negative infinity, the curve approaches (tends to) zero (but never actually gets there).

The y-intercept is the y-coordinate of the point where the curve crosses the y-axis, i.e. when x = 0.  If you input x = 0 into the function y = 5^x you get y = 1.  Therefore, the y-intercept of y = 5^x is y = 1