Question

PLSSS HELP
State the equation of the exponential function that has the
following features. (2 marks)
• It has the x-axis as an asymptote.
• It passes through (0,—i), (—1,—3), and (—2,—9).

Answer 1

An exponential function that has the x-axis as an asymptote, and It passes through (0,—i), (—1,—3), and (—2,—9) is y=-(1/3)ˣ.

What is an exponential function?

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

$y=ab^x$

Here, x is the variable in the power of a number.

State the equation of the exponential function that has the following features.

• It has the x-axis as an asymptote.
• It passes through (0,—1), (—1,—3), and (—2,—9). For the point (0,-1)

$-1=ab^{(0)}\\-1=a\times1\\a=-1$

For the point (-1,-3)

$-3=ab^{(-1)}\\-3=\dfrac{a}{b}$

Put, the value of -1 in the above equation,

$-3=\dfrac{-1}{b}\\b=\dfrac{1}{3}$

Thus, the exponential function,

$y=-1(\dfrac{1}{3})^x\\y=-\left (\dfrac{1}{3}\right)^x$

Hence, an exponential function that has the x-axis as an asymptote and It passes through (0,—i), (—1,—3), and (—2,—9) is y=-(1/3)ˣ.

Learn more about the exponential function here;

https://brainly.com/question/15602982

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