Page 177 - Algebra

Explanation:
1. y = f(x – 2)
It’s of the form y = f(x – h), the graph shifts right by 2 units The graph shifts to the right only in option c) and d)
y = f(x – 2) + 4
It’s of the form y = f(x) + h, the graph shifts upwards by 4 units. The graphs shift upwards in option b) and d)
Combining the two, the answer is option d).
2. The graph of a modulus function is defined as f(x) ≥ 0, for y = f(x)
and when f(x) < 0, the y = –f(x).
Therefore, the graph of the function will lie in quadrants I and II. The option is a) or d).
Furthermore, d) is of the form y = f(x) + 4
So, the correct answer is option a).
3. The graph is similar to y = f(x –h), it results in shifting the graph right by h unit. So, using y = 3x, you can sketch the graph using 4 units to the right.
4. The mirror image over the x-axis is the vertical reflection. y = –f(x)
y = 3x + 5
5. The mirror image over the y-axis is in horizontal reflection. y = f(–x)
So,
y = 3x – 5
6. y= f(– x) + 4
It’s of the form y =f(– x)
y =–f( x) + 4
7. y=f(x)
y = f(x + 7)
The graph is similar to y = f(x + h), it results in shifting the graph left by 7 units. Only in option a) and d) the graph shifts to the left.
But, only in option a) the graph shifts to the left by 7 units.
It results in horizontal reflection, and the graph shifts to the left.
Only in option c) and d) the graph shifts to the left
If you want to sketch y = f(x) + h, it results in shifting the graph vertically by h units.
Only in option c), it results in shifting the graph vertically by 4 units.
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Algebra I & II