Question

Which is the graph of the function y=2(4)^x

Answer 1

Answer:

is this highschool work?

Step-by-step explanation:

Answer 2

Answer:

See below  

Step-by-step explanation:

Here's one way to sketch the graph of a function.

Step 1. Find any zeroes.

(a) y-intercept

y = 2(4)^x     Let x = 0

  = 2(4)⁰

  = 2 × 1

  = 2

We have a point at (0,2).

(b) x-intercept

      y = 2(4)^x     Let y = 0

     0 = 2(4)^x     Divide each side by 2

     0 = (4)^x        Take the log of each side

log0 = xlog4

log(0) is undefined. There is no x-intercept.

Step 2. Identify any asymptotes

y = 2(4)^x

y can never be negative, so the x-axis is an asymptote.

Step 3. Calculate and plot a few points

Here's a table of a few points.

 x         y  

-3      0.0

-2      0.1

-1      0.5

0     2

1      8

2   32

3  128

Step 4. Check the end behaviour.

y = 2(4)^x

As x ⟶ ∞, y ⟶ ∞.

As x ⟶ -∞, y ⟶ 0

Step 5. Draw a smooth line through the points.

Your graph should look something like the one below.