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Anastaziya [24]
3 years ago
14

Exponential function f(x) has a y intercept of 3 and an x intercept of -2. the function is always increasing as the value of x i

ncreases, but the function never reaches y=4
would it be decreasing or increasing and will it point down or up?
PLZ ANSWER ASAP

Mathematics
1 answer:
Kisachek [45]3 years ago
7 0

Answer:

f(x)=-\left(\dfrac{1}{2}\right)^x+4

The exponential function is increasing and is concave down

Step-by-step explanation:

Let the equation of exponential function be

f(x)=a\cdot b^x+c,\ ,\ b>0

1. Exponential function f(x) has a y intercept of 3, so the graph of f(x) passes through the point (0,3). Thus,

3=a\cdot b^0+c\\ \\3=a+c

2. Exponential function f(x) has an x intercept of -2, so the graph of f(x) passes through the point (-2,0). Thus,

0=a\cdot b^{-2}+c\\ \\0=\dfrac{a}{b^2}+c

3. Function is always increasing as the value of x increases, but the function never reaches y=4, so

c=4

Hence,

\left\{\begin{array}{l}a+4=3\\ \\\dfrac{a}{b^2}+4=0\end{array}\right.\Rightarrow \left\{\begin{array}{l}a=-1\\ \\\dfrac{-1}{b^2}+4=0\end{array}\right.\Rightarrow \left\{\begin{array}{l}a=-1\\ \\b^2=\dfrac{1}{4}\end{array}\right.

So,

a=-1,\\ \\b=\dfrac{1}{2},\\ \\c=4,\\ \\f(x)=-\left(\dfrac{1}{2}\right)^x+4

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