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)=

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 $g(x)$. \[ g(x)= \]
failed

Solution

failed
failed

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: $g(x) = -(x+3) - 1 = -x - 3 - 1 = -x - 4$

Final Answer

$g(x) = -x - 4$

Was this solution helpful?
failed
Unhelpful
failed
Helpful