Explanation
The formulas for the transformations mentioned in the problem are:
• Reflection over the x-axis: f(x) → g(x) = -f(x),
,
• Shift down by a units (a > 0): f(x) → g(x) = f(x) - a,
,
• Shift left by b units (b > 0): f(x) → g(x) = f(x + b),
,
• Vertical stretch by a factor k: f(x) → g(x) = k f(x).
In this problem, we have the transformation:
[tex]f(x)=x\rightarrow g(x)=-5(x+3)-8.[/tex]
Comparing this expression with the transformations above, we identify:
• a ,reflection over the x-axis, due to the minus sign in front of 5,
,
• a ,shift down by 8 units,,
,
• a shift left by 3 units,,
,
• a ,vertical stretch by a factor of 5,.
We see that the only transformation not made is a shift right by 3 units.
Answer
C. Shift right 3 units
