The graph of y =1/x
is vertically stretched by a factor of 3, reflected across the y-axis and shifted to the left by 2 units. What is the function of the resulting graph?
y=3/x-2
y=-3/x+2
y=1/3x-6
y=-1/3x+6
my answer is B
stretch: 3/x
reflect: 3/(-x) = -3/x
shift: -3/(x+2)
who ever disliked Steve, I hope you're blanket is square
the graph was shifted from 6 units left and 5 units down the graph was also vertically reflected about the x axis what is the function
Well, I hate to burst your bubble, but your answer is not quite right. Let me show you why.
The original function is y = 1/x.
First, we vertically stretch the graph by a factor of 3. This means the new function has a vertical stretch of 3, resulting in y = 3(1/x), which simplifies to y = 3/x.
Next, we reflect the graph across the y-axis. This means we replace x with -x in the equation. Therefore, our new function becomes y = 3/(-x).
Lastly, we shift the graph 2 units to the left. So we replace x with (x + 2) in the equation. Our final function is y = 3/(-(x + 2)).
Simplifying this, we get y = -3/(x + 2).
That's the correct answer, my friend. It's option D, not B. Better luck next time!
To find the function of the resulting graph, we need to apply the given transformations step by step to the original function y = 1/x.
1. Vertically stretched by a factor of 3: Multiply the original function by 3. This gives us y = 3(1/x) = 3/x.
2. Reflected across the y-axis: Negate the x-term in the function. This gives us y = -3/x.
3. Shifted to the left by 2 units: Subtract 2 from the x-term. This gives us y = -3/(x-2).
Therefore, the function of the resulting graph is y = -3/(x-2). Comparing this with the options given, your answer of B is correct.