Question

the function $f(x) = \frac{3}{4}(10)^{-x}$ is reflected across the $x$-axis to create the function $g(x)$. which ordered pair is on $g(x)$?
$(-2, 75)$
$(2, -\frac{3}{400})$
$(3, -750)$
$(-3, -\frac{3}{4000})$

Explanation:

Step1: Define reflected function

Reflecting $f(x)$ over the x-axis gives $g(x) = -f(x)$. Substitute $f(x)$:
$g(x) = -\frac{3}{4}(10)^{-x}$

Step2: Test each ordered pair

For $(-2, 75)$:

Substitute $x=-2$ into $g(x)$:
$g(-2) = -\frac{3}{4}(10)^{-(-2)} = -\frac{3}{4}(10^2) = -\frac{3}{4}(100) = -75
eq 75$

For $(-3, -\frac{3}{4000})$:

Substitute $x=-3$ into $g(x)$:
$g(-3) = -\frac{3}{4}(10)^{-(-3)} = -\frac{3}{4}(10^3) = -\frac{3}{4}(1000) = -750
eq -\frac{3}{4000}$

For $(2, -\frac{3}{400})$:

Substitute $x=2$ into $g(x)$:
$g(2) = -\frac{3}{4}(10)^{-2} = -\frac{3}{4} \cdot \frac{1}{10^2} = -\frac{3}{4} \cdot \frac{1}{100} = -\frac{3}{400}$

For $(3, -750)$:

Substitute $x=3$ into $g(x)$:
$g(3) = -\frac{3}{4}(10)^{-3} = -\frac{3}{4} \cdot \frac{1}{10^3} = -\frac{3}{4000}
eq -750$

Answer:

$(2, -\frac{3}{400})$