Questions: What is the correct graph for the exponential function? f(x)=-3(1 / 4)^(x-3)+2

What is the correct graph for the exponential function? f(x)=-3(1 / 4)^(x-3)+2
Transcript text: What is the correct graph for the exponential function? \[ f(x)=-3(1 / 4)^{x-3}+2 \]
failed

Solution

failed
failed

Solution Steps

Step 1: Analyze the function

The function is f(x) = -3(1/4)^(x-3) + 2. This is an exponential function with a base of 1/4 (meaning it's decaying), a vertical reflection due to the -3, a horizontal shift 3 units to the right, and a vertical shift 2 units up.

Step 2: Identify key features
  • Horizontal Asymptote: y = 2 (due to the vertical shift).
  • y-intercept: Calculate f(0) = -3(1/4)^(-3) + 2 = -3 * 4^3 + 2 = -192 + 2 = -190. The y-intercept is very low.
  • General Shape: Because of the negative coefficient, the graph will be below the asymptote. It will approach the asymptote as x increases and decrease rapidly as x decreases.
Step 3: Compare to the graphs

Only graph 'b' has a horizontal asymptote around y=2 and reflects the other described properties. Graph 'a' has an asymptote close to y=0 and isn't reflected across a horizontal axis.

Final Answer

b

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Question 7 (1 point) A student is making a titration curve. To do so, they added 25.00 mL of 0.2470 M HCl to a flask. They then added 49.14 mL of 0.1170 M NaOH to the flask. What is the pH at this point in the titration curve? 3.1117 1.9343 2.2406 3.3436 1.6537
failedAnswered
The rate of a certain reaction is given by the following rate law: rate = k[H2]^2[NH3] Use this information to answer the questions below. What is the reaction order in H2? What is the reaction order in NH3? What is overall reaction order? At a certain concentration of H2 and NH3, the initial rate of reaction is 91.0 M / s. What would the initial rate of the reaction be if the concentration of H2 were doubled? Round your answer to 3 significant digits. The rate of the reaction is measured to be 0.330 M / s when [H2]=1.3 M and [NH3]=1.4 M. Calculate the value of the rate constant. Round your answer to 2 significant digits.
failedAnswered
Write each number in scientific notation. 5) 6.7
failedAnswered
What is the plasmids role in survival in extreme conditions? They hold the main genetic content of the bacteria They are junk DNA and does usually not serve a purpose They can encode for proteins that provide additional benefits for the bacteria to survive the local environment They carry genes coding for ribosomes which are essential for organisms
failedAnswered
Question 9 (2 points) What type of structures can be visualized using ultrasonography? A) Dense organs, such as bones. B) Air-filled organs, such as lungs. C) Soft internal structures, such as fetuses. D) Microscopic structures, such as mitochondria. Question 10 (2 points) The activities of an anatomist consist of , whereas those of a physi consist of