Question

What is the effect on the graph of f(x)=1x
when it is replaced by the function k(x)=98x
?(1 point)
Responses

It is vertically compressed by a factor of 8.
It is vertically compressed by a factor of 8.

It is vertically stretched by a factor of 98
.
It is vertically stretched by a factor of 9 eighths.

It is vertically compressed by a factor of 98
.
It is vertically compressed by a factor of 9 eighths.

It is vertically stretched by a factor of 9.
It is vertically stretched by a factor of 9.

Answer 1

To analyze the effect of replacing the function \( f(x) = x \) with the function \( k(x) = 98x \), we need to consider the effects of the coefficient of \( x \) on the graph.

The original function \( f(x) = x \) has a slope of 1, which means it increases at a 45-degree angle. When we look at the function \( k(x) = 98x \), the coefficient 98 means that for every unit increase in \( x \), \( k(x) \) increases by 98 units.

This means:

- The graph of \( k(x) \) will be vertically stretched compared to \( f(x) \):
- It is stretched by a factor of 98 because the output value of \( k(x) \) is 98 times greater than that of \( f(x) \) for each \( x \).

So, the correct response is:

**It is vertically stretched by a factor of 98.**