2x − 3 < x + 2
∴ x − 3 < 2
∴ x < 5
x + 2 ≤ 3x + 5
∴ 2 ≤ 2x + 5
∴ -3 ≤ 2x
∴ -3/2 ≤ x
<span>-3/2 ≤ x < 5</span>
Look at the graph below carefully
Observe the results of shifting ={2}^{x}f(x)=2x
vertically:
The domain, (−∞,∞) remains unchanged.
When the function is shifted up 3 units to ={2}^{x}+3g(x)=2x +3:
The y-intercept shifts up 3 units to (0,4).
The asymptote shifts up 3 units to y=3y=3.
The range becomes (3,∞).
When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 x −3:
The y-intercept shifts down 3 units to (0,−2).
The asymptote also shifts down 3 units to y=-3y=−3.
The range becomes (−3,∞).
Answer:
Distance to appointment point = 5 miles
Step-by-step explanation:
Let s be the distance to the appointment point,
We have Maria drove to a business appointment at 50mph in the morning.
Time taken in the morning

Her average speed on the return trip in the afternoon was 40 mph.
Time taken in the afternoon

Given that the return trip took 1/4hr longer because of traffic.
That is

Substituting

Distance to appointment point = 5 miles