Question

How do you translate a graph up or down ?

Answer 1

Hint: When we draw the graph of f(x) , if we shift the graph of f(x) k units upward, then the new graph would be of f(x) +k similarly if we shift the graph k units downward, the new graph would be of f(x)-k .

Complete step by step answer:
We translate a graph up by shifting every point on the graph upwards by some units and we translate a graph down by shifting every point on the graph downward by some units.
If we shift the curve f k units upward the new curve will be of f(x)+k, let’s take an example lets draw the graph of $f\left( x \right)={{x}^{2}}$ and shift the graph upward by 4 units

We can see that the green curve is of $f\left( x \right)={{x}^{2}}$ and if we shift the curve 4 units upward we will get the blue curve which is $f\left( x \right)={{x}^{2}}+4$ , if we shift the green curve 4 units downward we will get the curve for $f\left( x \right)={{x}^{2}}-4$.

Note:
If we translate any curve right or left that means if we have a curve f(x) and we shift the curve k units towards right then we will get the curve for f(x-k) and if we shift the curve k units towards left we will get the curve for f(k+x) . Do not get confused between f(x)+k and f(x+k) . If $f\left( x \right)={{x}^{2}}$ , then $f\left( x \right)+k$ is equal to ${{x}^{2}}+k$ and $f\left( x+k \right)$ is equal to ${{\left( x+k \right)}^{2}}$