Question

Given the graph of a function f. Identify the function by name. Then Graph, state the domain and range, use set notation forA) 1/2f(x)B) 2f(x)

Answer 1

From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:

`f(x)\text{ = }x^2`

The graph of (a) 1/2 f(x):

This implies that f(x) is compressed vertically by a factor of 1/2.

Using the points:

(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)

The graph of the function using a graphing calculator is shown below:

The graph of (b) 2 f(x)

This implies that the original function was stretched vertically by a factor of 2

Using the points:

(-4, 32), (-2, 8), (0,0), (2,8), (4,32)

The graph using a graphing calculator is shown below:

The domain:

This is a set of allowable x-values

Using interval notation:

`(-\infty,\text{ }\infty)\text{ or All real numbers}`

The range:

This is a set of allowable y-values:

Using interval notation:

`\lbrack0,\text{ }\infty)\text{ }`