Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?Responses-4negative 4-2negative 200
Question
Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?Responses-4negative 4-2negative 200
Solution
The point of intersection of two graphs is the solution to the equation that sets the two functions equal to each other. So, we need to solve the equation g(x) = h(x) for x.
Step 1: Set the two functions equal to each other:
4x = 16x + 2
Step 2: Subtract 16x from both sides to get:
-12x = 2
Step 3: Divide both sides by -12 to solve for x:
x = 2 / -12 = -1/6
So, the x-coordinate of the point of intersection of the graphs of g and h is -1/6.
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