A cubic graph has the equation:
y = 3(x-1)(x+2)(x+5)
Write in similar form the equation of the graph after a translation ( 3)
Could you show me step-by step please?
You need to specify the direction of the translation, 3 units along +x, along -y ??
Translation along +y direction is simply adding a constant to the function.
Thus g(x) = f(x)+3 would shift f(x) upwards by three units.
On the other hand, g(x) = f(x-k) will shift the graph of f(x) k units to the right, i.e. in the direction of +x axis.
If you need further help, please post.
To translate the graph 3 units to the right, we need to replace every occurrence of "x" in the equation with "x - 3".
Let me show you the step-by-step process:
1. Start with the given equation: y = 3(x - 1)(x + 2)(x + 5)
2. Replace "x" with "x - 3" in the equation:
y = 3((x - 3) - 1)((x - 3) + 2)((x - 3) + 5)
3. Simplify each term within the equation:
y = 3(x - 4)(x - 1)(x + 2)
4. Now we can see the equation of the translated graph after a translation of 3 units to the right:
y = 3(x - 4)(x - 1)(x + 2)
Thus, the equation of the translated graph after a translation of 3 units to the right is y = 3(x - 4)(x - 1)(x + 2).
Sure! To translate a graph by a value of 3 units to the right, you need to replace each occurrence of 'x' in the original equation with 'x - 3'. Here's how you can do it step-by-step:
Step 1: Start with the original equation: y = 3(x-1)(x+2)(x+5).
Step 2: Replace each occurrence of 'x' with 'x - 3':
y = 3((x - 3) - 1)((x - 3) + 2)((x - 3) + 5).
Step 3: Simplify the expression inside the brackets:
y = 3(x - 4)(x - 1)(x + 2).
Therefore, the equation of the graph after a translation by 3 units to the right is:
y = 3(x - 4)(x - 1)(x + 2).
This new equation represents the same cubic graph, but shifted 3 units to the right compared to the original graph.