Question

the function f(x)=(14)x by moving the key points. You can only graph integer points, for example you cannot plot the point (−1,14) .

Answer 1

The graph of the shifted function will pass through the new key point

• - (0, 0)
• - (1, 1/4)
• - (-1, -1/4)
• - (2, 1/2)
• - (-2, -1/2)

To graph the function
`\(f(x) = (1)/(4)x\)` using integer points, we can choose some key x-values and calculate the corresponding y-values. Here are some points to consider:

`1. When \(x = 0\): \(f(0) = (1)/(4)(0) = 0\)\\2. When \(x = 1\): \(f(1) = (1)/(4)(1) = (1)/(4)\)\\3. When \(x = -1\): \(f(-1) = (1)/(4)(-1) = -(1)/(4)\)\\4. When \(x = 2\): \(f(2) = (1)/(4)(2) = (1)/(2)\)\\5. When \(x = -2\): \(f(-2) = (1)/(4)(-2) = -(1)/(2)\)`

Now, we can plot these points on a graph:

- (0, 0)

- (1, 1/4)

- (-1, -1/4)

- (2, 1/2)

- (-2, -1/2)

These points will give you an idea of the behavior of the function. If you're using graphing software or a calculator, inputting these points and connecting them will allow you to visualize the linear nature of the function
`\(f(x) = (1)/(4)x\)`.

Therefore the graph of the shifted function will pass through the new key point

- (0, 0)

- (1, 1/4)

- (-1, -1/4)

- (2, 1/2)

- (-2, -1/2)