Sketch the graph of the given function. then state the function’s domain and range. (note: the scale on the axes are not the same.) y = 10(3)x

Here's what I get.

Step-by-step explanation:

A. Sketch the graph

1. Find any zeroes.

(a) y-intercept

Let x = 0

y = 10(3)⁰ = 10 × 1 = 10

We have a point at (0, 10).

(b) x-intercept

Let y = 0

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

2. Identify any asymptotes

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

3. Plug in and plot a few points

Here's a table of a few points.

4. Check the end behaviour.

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.

B. Domain

The domain is the set of all possible x-values that will make the function work.

x can take any value from -∞ to ∞

The domain is (-∞, ∞).

C. Range

The range is the spread of the y-values.

We see from the graph that y can have any positive value except zero.

The range is (0, ∞).

step-by-step explanation:

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