Question

find the value of f(7).
y = f(x)
answer attempts 1 out of 4

Explanation:

Step1: Identify the right - hand line

The graph of \(y = f(x)\) has a right - hand segment from the peak (at \(x = 1\), \(y=9\)) to the x - intercept at \((10,0)\). We need to find the equation of this line. The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(1,9)\) and \((x_2,y_2)=(10,0)\). Then \(m=\frac{0 - 9}{10 - 1}=\frac{-9}{9}=- 1\).

Step2: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Using the point \((1,9)\) and \(m=-1\), we have \(y-9=-1(x - 1)\), which simplifies to \(y=-x + 1+9=-x + 10\).

Step3: Evaluate \(f(7)\)

To find \(f(7)\), we substitute \(x = 7\) into the equation \(y=-x + 10\). So \(y=-7 + 10 = 3\).

Answer:

\(3\)