Question

remember***
f(-3) means -3 is your input and you plug it in for x
f(x) = -3 means that your whole function is = to -3 and you plug into the y.
guided practice 1: find the value of f(-5).
y = f(x)
teacher example 2:
guided practice 2:
guided practice 3:
answer:

Explanation:

Step1: Understand \( f(-5) \)

\( f(-5) \) means find the \( y \)-value when \( x = -5 \) on the graph \( y = f(x) \).

Step2: Locate \( x = -5 \)

On the \( x \)-axis, find \( x = -5 \). Then, move vertically to intersect the graph of \( y = f(x) \).

Step3: Determine the \( y \)-value

The graph at \( x = -5 \) is on the linear part (the left - slanting line). The equation of the left - slanting line: we can see it passes through \( (0, - 1) \)? Wait, no, let's check the slope. Wait, when \( x=-5 \), looking at the graph, the left line: let's take two points. When \( x = 0 \), what's \( y \)? Wait, the left line: when \( x=-2 \), \( y = 0 \)? Wait, no, maybe better to see the line. Wait, the left line goes from, say, when \( x=-10 \), \( y = 9 \)? No, wait, the graph: the left line (the upper line) has a slope. Wait, actually, when \( x=-5 \), we can see that the \( y \)-value is 4? Wait, no, let's re - examine. Wait, the left line: let's see, when \( x = 0 \), the line crosses the \( y \)-axis? Wait, no, the left line (the non - V part) is a straight line. Let's find the equation of the left line. Let's take two points on the left line. Let's say when \( x=-2 \), \( y = 0 \) (intersection with the \( x \)-axis) and when \( x = 0 \), \( y=-1 \)? No, that doesn't seem right. Wait, maybe the left line has a slope of \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Wait, maybe a better way: when \( x=-5 \), we move up from \( x=-5 \) to the left line. Looking at the graph, the left line (the upper linear segment) at \( x=-5 \), the \( y \)-value is 4? Wait, no, let's count the grid. Wait, the \( y \)-axis has marks: 10, 8, 6, 4, 2, 0, - 2, - 4, - 6, - 8, - 10. The \( x \)-axis: - 10, - 8, - 6, - 4, - 2, 0, 2, 4, 6, 8, 10. The left line (the upper line) when \( x=-5 \), the \( y \)-value is 4? Wait, no, let's see: the left line (the line before the V - shape) has a slope. Let's take two points: when \( x=-2 \), \( y = 0 \) (since it crosses the \( x \)-axis at \( x=-2 \)) and when \( x = 0 \), \( y=-1 \)? No, that would be slope \( m=\frac{-1 - 0}{0+2}=-\frac{1}{2}\). Then the equation is \( y-0=-\frac{1}{2}(x + 2) \), so \( y=-\frac{1}{2}x - 1 \). Now, plug \( x=-5 \) into this equation: \( y=-\frac{1}{2}(-5)-1=\frac{5}{2}-1=\frac{3}{2}=1.5 \)? No, that's not matching. Wait, maybe I misread the graph. Wait, the original graph: the left line (the upper line) is a straight line going from, say, \( x=-10 \) to \( x = 2 \) (before the V - shape). Wait, maybe the correct way is to look at the graph: when \( x=-5 \), the \( y \)-value is 4? Wait, no, let's check again. Wait, the user's graph: the left line (the upper line) at \( x=-5 \), the \( y \)-coordinate is 4? Wait, maybe I made a mistake. Wait, actually, looking at the graph, the left line (the non - V part) has a slope of - 1? Wait, if \( x=-5 \), and the line passes through \( (0, - 1) \) and \( (-5, 4) \), because the slope would be \( \frac{4-(-1)}{-5 - 0}=\frac{5}{-5}=-1 \). Yes, that works. So the equation is \( y=-x - 1 \). Then when \( x=-5 \), \( y=-(-5)-1=5 - 1 = 4 \). Wait, no, \( y=-x - 1 \), when \( x=-5 \), \( y=-(-5)-1=5 - 1 = 4 \). Yes, that's correct. So \( f(-5)=4 \)? Wait, no, wait, if the line is \( y=-x - 1 \), when \( x = 0 \), \( y=-1 \), when \( x=-5 \), \( y = 5 - 1 = 4 \). Yes, that matches. So the value of \( f(-5) \) is 4.

Answer:

\( 4 \)