We are given a linear function $f$ such that $f(7) = 14$. We need to: 1. Determine the expression of $f(x)$.

1. Problem Description

We are given a linear function $f$ such that $f(7) = 14$. We need to:

1. Determine the expression of $f(x)$.

2. Find the number whose image is 21 under the function $f$.

3. Sketch the graph of $f$.

2. Solution Steps

1. Since $f$ is a linear function, it has the form $f(x) = ax$, where $a$ is a constant.

We are given $f(7) = 14$. Substituting $x=7$ into the expression for $f(x)$, we have $f(7) = a(7) = 7a$.

Therefore, $7a = 14$, which means $a = \frac{14}{7} = 2$.

Thus, the expression for $f(x)$ is $f(x) = 2x$.

2. We want to find $x$ such that $f(x) = 21$. Since $f(x) = 2x$, we have $2x = 21$.

Dividing both sides by 2, we get $x = \frac{21}{2} = 10.5$.

So, the number whose image is 21 is 10.

5.

3. To sketch the graph of $f(x) = 2x$, we need to plot at least two points.

We already know $f(0) = 2(0) = 0$, so the point $(0,0)$ lies on the graph.

We are given $f(7) = 14$, so the point $(7,14)$ lies on the graph.

The graph of $f$ is a straight line passing through the origin $(0,0)$ and the point $(7,14)$.

The line is often denoted as $(D)$.

3. Final Answer

1. The expression for $f(x)$ is $f(x) = 2x$.

2. The number whose image is 21 is 10.

5.

3. The graph of $f$ is the line passing through $(0,0)$ and $(7,14)$.