Question

find the value of $f(7)$.
$y = f(x)$
answer attempt 1 out of 2

Explanation:

Step1: Identify the right - hand line

The right - hand part of the graph \(y = f(x)\) (for \(x\geq1\) approximately, from the graph) is a straight line. We can find its equation. First, find two points on this line. We can see that it passes through \((1, - 2)\) and \((2, - 1)\) (or we can also use the x - intercept and another point). Let's find the slope \(m\) of the line. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: when \(x = 1\), \(y=-2\); when \(x = 2\), \(y=-1\). Then \(m=\frac{-1-(-2)}{2 - 1}=\frac{-1 + 2}{1}=1\).

Step2: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Using the point \((1,-2)\) and \(m = 1\), we have \(y-(-2)=1\times(x - 1)\), which simplifies to \(y+2=x - 1\), so \(y=x-3\).

Step3: Evaluate \(f(7)\)

Now, to find \(f(7)\), we substitute \(x = 7\) into the equation \(y=x - 3\). So \(y=7-3=4\).

Answer:

\(4\)