ACT · Math · Preparing for Higher Math
Evaluar funciones, composición, inversas, crecimiento exponencial y funciones trigonométricas.
Notación, composición, inversas, exponenciales y trigonométricas.
$f(x)=2x2-3x+1$ → $f(-2)=8+6+1=15$.
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
If $f(x)=2x2-3x+1$, what is the value of $f(-2)$ ?
Respuesta correcta: C. $15$
$f(-2)=2(-2)2-3(-2)+1=2(4)+6+1=15$.
$-1$ treats $(-2)2$ as $-4$. 3 subtracts 6 instead of adding it $(8-6+1)$. 23 squares $2\cdot(-2)$ instead of only $-2$: $(-4)2+6+1$.
What is the period of the function $y=3\sin(2x)-1$ ?
Respuesta correcta: B. $\pi$
For $y=a\sin(bx)+d$, the period is $\frac{2\pi}{|b|}$. Here $b=2$, so the period is $\frac{2\pi}{2}=\pi$. The 3 changes the amplitude and the $-1$ shifts the graph down; neither affects the period.
$\frac{\pi}{2}$ divides by 4 instead of 2. $2\pi$ is the period of $\sin x$ without the factor 2. $4\pi$ multiplies by 2 instead of dividing.
If $3x=5$ and $9y=20$, what is the value of $3\,y-x$ ?
Respuesta correcta: B. $\frac{2\sqrt{5}}{5}$
Write everything with base 3. Since $9y=\left(32\right)y=32y=20$, we get $3y=\sqrt{20}=2\sqrt5$. Then $3\,y-x=\frac{3y}{3x}=\frac{2\sqrt5}{5}\approx0.89$.
$4$ treats $9y$ as if it were $3y$ ($\frac{20}{5}$), the trap. $\frac45$ is $\frac{9y}{9x}=\frac{20}{25}$, which is $9\,y-x$, not $3\,y-x$. $2$ takes the square root of the wrong ratio $\frac{20}{5}$.