Answer:
Exponential function
[tex]y=1.25(2)^x[/tex]
Step-by-step explanation:
Definitions
Asymptote: a line that the curve gets infinitely close to, but never touches.
Hole: a point on the graph where the function is not defined.
Polynomial Function
[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]
An equation containing variables with non-negative integer powers and coefficients, that involves only the operations of addition, subtraction and multiplication.
A continuous function with no holes or asymptotes.
Rational Function
[tex]f(x)=\dfrac{h(x)}{g(x)}[/tex]
An equation containing at least one fraction whose numerator and denominator are polynomials.
A rational function has holes and/or asymptotes.
- A rational function has holes where any input value causes both the numerator and denominator of the function to be equal to zero.
- A rational function has vertical asymptotes where the denominator approaches zero.
- If the degree of the numerator is smaller than the degree of the denominator, there will be a horizontal asymptote at y = 0.
- If the degree of the numerator is the same as the degree of the denominator, there will be a horizontal asymptote at y = ratio of leading coefficients.
- If the degree of the numerator is exactly one more than the degree of the denominator, slant asymptotes will occur.
Logarithmic Function
[tex]f(x) =\log_ax[/tex]
A continuous function with a vertical asymptote.
A logarithmic function has a gradual growth or decay.
Exponential Function
[tex]f(x)=ab^x[/tex]
The variable is the exponent.
A continuous function with a horizontal asymptote.
An exponential function has a fast growth or decay.
