A classmate claims that the Junction g(x)=-3e^x-2+6 is the parent function of f(x)=e^x reflected across the y -axis, vertically compressed by a factor of 3 translated to the left 2 units, and translated up 6 units. Explain what the classmate described incorrectly and describe g(x) as a series of transformations of f(x) Part 1 out of 2 Identify which transformations the classmate described incorrectly. Reflected across the y -axis. (select) square Vertically compressed by a factor of 3. (select) square Translated to the left 2 units. (select) square Translated up 6 units (select) square

## Step 1: Analyze the Transformation related to the x-variable<br />### The function $g(x)$ has the term $e^{x-2}$, which represents a horizontal translation. A term of $x-2$ shifts the graph 2 units to the *right*, not to the left.<br /><br />## Step 2: Analyze the Transformations related to the entire function<br />### The function $g(x)$ has a coefficient of -3 multiplied by the exponential term. The negative sign indicates a reflection across the x-axis, not across the y-axis. The 3 represents a vertical *stretch* by a factor of 3, not a compression. The +6 added to the function represents a vertical translation of 6 units upwards, which is correct.