intercepts of f(x)=-sqrt(x)+3 — step-by-step solution

On the horizontal axis, y = 0: solve

- \sqrt{x} + 3 = 0

⇥1) Let's solve in

ℝ

- \sqrt{x} + 3 = 0

⇥2) The numeric value of:

-1 \cdot (-3)

is:

⇥

3

⇥Isolate the square root:

\sqrt{x} = 3

. Since the right side is nonnegative, square both sides:

⇥

x = {(-1 \cdot (-3))}^{2}

⇥ⓘ Two minus signs cancel out, the product of two negative numbers is positive:

-1 \cdot (-3)

3

⇥

x = 3^{2}

⇥ⓘ An integer power is a repeated product:

3^{2}

3 \cdot 3

9

⇥Candidates, pending the domain check:

x = 9

⇥ For the expression

- \sqrt{x}

to be defined, we must have:

x \geq 0

⇥Domain constraints:

x \geq 0

The graph crosses the horizontal axis at

(9, 0)

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

⇥

- \sqrt{0} + 3

⇥ⓘ Adding 0 changes nothing:

0 + 3

3

⇥

3

▶Axis intercepts:

{(9, 0), (0, 3)}