For a transverse wave on a string, the string displacement is described by $y(x,t)=f(x-at)$ where $f$ represents a function and 'a' is a negative constant. Then which of the following are CORRECT statements. 

$y(x,0)=f\left(x\right)$ so shape of string at $t=0$ is given by $y=f\left(x\right)$.

As velocity of wave $\frac{\mathrm{dx}}{\mathrm{dt}}=+\mathrm{a}$ is a constant, so shape of string doesn't change or we can say $(x-at)$ is constant, so shape of string remains same.

As ‘a’ is a negative constant, so $\frac{\mathrm{dx}}{\mathrm{dt}}=$ negative and hence wave is moving along negative x direction  speed $=-\text{'}a\text{'}$ as speed can't be negative.