Explanation:
1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given
2. ∆CRH ~ ∆HSC — AA similarity theorem
3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent
4. CH ≅ HC — reflexive property of congruence
5. ∆CRH ≅ ∆HSC — SAS congruence theorem
6. CR ≅ HS — CPCTC
The parent function of g(x) = |x - 7| +6 is f(x) = |x|
<h3>How to determine the parent function?</h3>The function is given as:
g(x) = |x - 7| +6
The above function is an absolute function, and the parent function is f(x) = |x|
Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|
<h3>The reflection</h3>When f(x) is reflected across the x-axis, we have:
f'(x) = -|x|
When f(x) is reflected across the y-axis, we have:
f'(x) = |x|
<h3>Stretching and Compression</h3>When f(x) is stretched horizontally by a factor k
g'(x) = |kx|
When f(x) is stretched vertically by a factor k
g'(x) = k|x|
<h3>Horizontal Shift</h3>When f(x) is shifted horizontally by k units
f'(x) = |x ± k|
<h3>Vertical Shift</h3>When f(x) is shifted vertical by k units
f'(x) = |x| ± k
See attachment for the graph of g(x)
Read more about function transformation at:
#SPJ1
