Question

Let f(x) represent a function.

Which descriptions match the given transformations?

Drag and drop the answers into the boxes.

Answer 1

Answer:

For $f(x+\frac{5}{4})$, $f(x)$ is translated $\frac{5}{4}$ units left.

For $f(x)-\frac{5}{4}$, $f(x)$ is translated $\frac{5}{4}$ units down.

Step-by-step explanation:

The transformation of $f(x)\rightarrow f(x+C)$ means that the graph shift to left by C units if C is positive number and shifts to right by C units if C is a negative number.

The transformation of $f(x)\rightarrow f(x)+C$ means that the graph shifts up by C units if C is positive number and shifts down by C units if C is a negative number.

Here, in the transformation of $f(x)\rightarrow f(x+\frac{5}{4}),C = \frac{5}{4}>0$, so, the function translates left by $\frac{5}{4}$ units.

Similarly, in the transformation of $f(x)\rightarrow f(x)-\frac{5}{4},C = -\frac{5}{4}<0$, so, the function translates down by $\frac{5}{4}$ units.