the table gives selected key features from a transformed function g(x) = tan x + d and its original function…
the table gives selected key features from a transformed function g(x) = tan x + d and its original function f(x) = tan x. key feature f(x) g(x) inflection point (0, 0) (0, 12.4) concave up (0, π/2) (0, π/2) vertical asymptotes π/2 + kπ π/2 + kπ describe the transformation. left 12.4 units right 12.4 units up 12.4 units down 12.4 units
Answer
Explanation:
Step1: Analyze inflection - point change
The inflection - point of $f(x)=\tan x$ is $(0,0)$ and for $g(x)=\tan x + d$ is $(0,12.4)$. The $x$ - coordinate remains the same and the $y$ - coordinate changes from $0$ to $12.4$.
Step2: Recall function transformation rules
For a function $y = f(x)+d$, when $d>0$, the graph of the function is shifted vertically upwards by $d$ units. Here, since the $y$ - value of the inflection - point has increased from $0$ to $12.4$, the function $g(x)$ is obtained by shifting $f(x)$ upwards.
Answer:
Up 12.4 units