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A function is exponential and satisfies the following conditions:
MATHEMATICS · Single correct · GCSE · Mathematics · Graphs · Graphs
Problem
A function
f
f
f
is exponential and satisfies the following conditions: (i)
f
f
f
is decreasing on
R
\mathbb{R}
R
. (ii) The
y
y
y
-intercept is
4
4
4
. (iii) The horizontal asymptote is
y
=
0
y=0
y
=
0
. Which of the following could be
f
(
x
)
f(x)
f
(
x
)
? (a)
4
⋅
2
x
4\cdot2^{x}
4
⋅
2
x
(b)
4
+
(
1
2
)
x
4+\left(\tfrac12\right)^{x}
4
+
(
2
1
)
x
(c)
4
⋅
(
1
2
)
x
4\cdot\left(\tfrac12\right)^{x}
4
⋅
(
2
1
)
x
(d)
4
⋅
(
1
2
)
x
+
1
4\cdot\left(\tfrac12\right)^{x}+1
4
⋅
(
2
1
)
x
+
1
Related theory
Exponential Functions
Exponential and Logarithmic Functions
Functions
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