# Mixed Transformations - Horizontal

- Author:
- Peter Sassman

Consider the two functions, f(x) and g(x), shown below, which will have two transformations: horizontal translation and horizontal stretch.
f(x) will be stretched first, followed by a translation.
g(x) will be translated first, followed by a stretch.
Play around with this, and then answer the questions below.

**Question 1:**Does the order of horizontal translations and horizontal stretches affect each other?

**Question 2:**Consider a horizontal stretch by a factor of 0.5, and a horizontal translation by 4 units to the right. Find the equation for f(x) and g(x). Are they equal?

**Question 3:**Consider a horizontal reflection, and a horizontal translation by 2 units to the right. Find the equation for f(x) and g(x). Are they equal?

**Question 4:**Generalize: Consider a horizontal stretch by a factor of 1/b, and a horizontal translation c units to the right. Find the equation for f(x) and g(x).

**Question 5:**Consider the equation h(x)=

**A:**We do a stretch first;

**B:**We do a translation first.

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