tmua 2017 Q7

tmua · Uk · paper2 1 marks Exponential Functions True/False or Multiple-Statement Verification

The graphs of two functions are shown here:

$y = a ^ { x }$ is shown with a solid line, where $a$ is a positive real number
$y = f ( x )$ is shown with a dashed line

Which of the following statements $( \mathbf { 1 } , \mathbf { 2 } , \mathbf { 3 } , \mathbf { 4 } )$ could be true?
$1 f ( x ) = b ^ { x }$ for some $b > a$
$2 f ( x ) = b ^ { x }$ for some $b < a$
$3 f ( x ) = a ^ { k x }$ for some $k > 1$
$4 f ( x ) = a ^ { k x }$ for some $k < 1$
A $\mathbf { 1 }$ only
B 2 only
C 3 only
D 4 only
E 1 and 3 only
F 1 and 4 only
G 2 and 3 only
H 2 and 4 only

& B

The graphs of two functions are shown here:

\begin{itemize}
  \item $y = a ^ { x }$ is shown with a solid line, where $a$ is a positive real number
  \item $y = f ( x )$ is shown with a dashed line
\end{itemize}

Which of the following statements $( \mathbf { 1 } , \mathbf { 2 } , \mathbf { 3 } , \mathbf { 4 } )$ could be true?

$1 f ( x ) = b ^ { x }$ for some $b > a$

$2 f ( x ) = b ^ { x }$ for some $b < a$

$3 f ( x ) = a ^ { k x }$ for some $k > 1$

$4 f ( x ) = a ^ { k x }$ for some $k < 1$

A $\mathbf { 1 }$ only

B 2 only

C 3 only

D 4 only

E 1 and 3 only

F 1 and 4 only

G 2 and 3 only

H 2 and 4 only

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20