Let g(x) be the reflection of f(x) = x 2 + 3 in the x-axis. what is the function rule for g(x)?

Step-by-step explanation:

The parent function is

Now, the function g(x) is obtained by reflecting the graph of f(x) about the x-axis.

When the parent function f(x) is reflected about the x-axis then the translated function is -f(x)

Therefore, we have g(x)=-f(x)

Hence, the equation of g(x) is

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west