Questions: The graph of f is translated a whole number of units horizontally and vertically to obtain the graph of g. The function f is defined by f(x)=-x. Write down the expression for g(x). g(x)=
Transcript text: The graph of $f$ is translated a whole number of units horizontally and vertically to obtain the graph of $g$.
The function $f$ is defined by $f(x)=-|x|$.
Write down the expression for $g(x)$.
\[
g(x)=
\]
Solution
Solution Steps
Step 1: Find the horizontal shift
The graph of $g(x)$ is shifted 3 units to the left compared to $f(x)$. This means we replace $x$ with $x+3$ in the original function.
Step 2: Find the vertical shift
The graph of $g(x)$ is shifted 1 unit down compared to $f(x)$. This means we subtract 1 from the function.
Step 3: Write the equation for g(x)
Combining the horizontal and vertical shifts, the equation for g(x) is:
$g(x) = -(x+3) - 1 = -x - 3 - 1 = -x - 4$