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

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.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.