intercepts of f(x)=4(3)^x — step-by-step solution

On the horizontal axis, y = 0: solve

4 \cdot 3^{x} = 0

⇥Let's solve in

ℝ

4 \cdot 3^{x} = 0

⇥We simplify the expression by

4

⇥⇥Let's solve in

ℝ

3^{x} = 0

⇥⇥In ℝ, a strictly positive number raised to any power stays strictly positive:

3^{x} > 0

, so

3^{x} = 0

has no solution

⇥⇥Solution:

x \in \emptyset

The graph does not cross the horizontal axis

On the vertical axis, x = 0: calculate f(0)

⇥

4 \cdot 3^{0}

⇥ⓘ Any nonzero number raised to the power 0 is 1:

3^{0}

1

⇥

4

▶Axis intercepts:

(0, 4)