Question

question 4 of 7
the graph of an exponential function is shown in the figure below.
the horizontal asymptote is shown as a dashed line.
find the domain and the range.
write your answers as inequalities, using x or y as appropriate.
domain:
range:

Explanation:

Question 3:

Step1: Calculate y for x=-2

Substitute $x=-2$ into $f(x)=\frac{5}{4}(2)^x$:
$\frac{5}{4}(2)^{-2} = \frac{5}{4} \times \frac{1}{4} = \frac{5}{16}$

Step2: Calculate y for x=-1

Substitute $x=-1$ into $f(x)=\frac{5}{4}(2)^x$:
$\frac{5}{4}(2)^{-1} = \frac{5}{4} \times \frac{1}{2} = \frac{5}{8}$

Step3: Calculate y for x=0

Substitute $x=0$ into $f(x)=\frac{5}{4}(2)^x$:
$\frac{5}{4}(2)^{0} = \frac{5}{4} \times 1 = \frac{5}{4}$

Step4: Calculate y for x=1

Substitute $x=1$ into $f(x)=\frac{5}{4}(2)^x$:
$\frac{5}{4}(2)^{1} = \frac{5}{4} \times 2 = \frac{5}{2}$

Step5: Calculate y for x=2

Substitute $x=2$ into $f(x)=\frac{5}{4}(2)^x$:
$\frac{5}{4}(2)^{2} = \frac{5}{4} \times 4 = 5$

Question 4:

Step1: Identify domain

Exponential functions have no restrictions on x-values, so all real numbers are allowed.

Step2: Identify range

The graph lies above the horizontal asymptote (dashed line, assumed to be $y=2$), so y is greater than 2.

Answer:

Question 3 (table values):

$x$	$y$
$-1$	$\frac{5}{8}$
$0$	$\frac{5}{4}$
$1$	$\frac{5}{2}$
$2$	$5$

Question 4:

Domain: $-\infty < x < \infty$
Range: $y > 2$